JP2017114199A - Folded structure allowing sheet foldable and protective cover made of folded structure allowing sheet foldable - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a folded structure capable of creating a plane body which can be developed into a three-dimensional shape for a solid with frequently repeating three-dimensional shapes and folded shapes formed of two directive double corrugated type developing structure bodies, without destroying the folded structure, by connecting them in different orientations according to the number of folds.SOLUTION: A folded structure solves a conventional problem by means determining an order of folding a developable plane body and changing angles and lengths in a deformation region to prevent basic figures from interfering with each other.SELECTED DRAWING: Figure 12

Description

The present invention relates to a foldable structure, and more particularly, to a foldable structure applying a so-called Miura fold (registered trademark) of a double corrugated expandable structure applying a development surface.

Furthermore, it relates to a protective cover that protects the object to be protected from dust, mold, pollen, yellow sand, PM2.5 particles, rain water, cold air, frost, or strong sunlight, and more specifically, bicycles, motorcycles, The present invention relates to a protective cover for an auto tricycle or an automobile.

Conventionally, a folding sheet known as Miura folding (registered trademark) is known (for example, see 1993 Utility Model Application Publication No. 25023 for a new folding method).
That is, the folding sheet extends in a direction intersecting with the vertical folding lines and a plurality of vertical folding lines that are parallel to each other and each fold line is formed by alternating continuous lines of mountain folds and valley folds. These fold lines that are zigzag fold lines that are adjacent to each other in the vertical direction are folded in opposite fold lines and horizontal fold lines that are valley fold lines. A basic region (consisting of four parallel quadruple linear segments adjacent to each other) partitioned by each lateral fold line cooperates with each other, and the deformation applied to one basic region is a deformation of the adjacent basic region In other words, the basic regions are in the same open / closed state, that is, the sheet can be folded and unfolded automatically only by approaching and separating the diagonal corners of the sheet. Since then, manufacturing methods have been proposed using the above structure.

For example, Patent Document 1 (Japanese Patent Application No. 2013-17004) has been devised which makes it possible to deploy and store a structure with a small driving amount. In addition, Patent Document 2 (Japanese Patent Laid-Open No. 2008-284860) and Patent Document 3 (Japanese Patent Laid-Open No. 2012-116656), which were devised by Prof. Miura, who also became the name of folding, have been devised. Patent Document 4 (Japanese Patent Application No. 2015-33772) is also devised.

In the idea of Patent Document 1 (Japanese Patent Application No. 2013-17004), it is an object to make it possible to deploy and store a structure with a small driving amount. , Something to be stored.

In the device of Patent Document 2 (Japanese Patent Application Laid-Open No. 2008-284860), an object having a two-dimensional spread, such as paper, can be folded or opened from four sides at once in synchronization with a single operation, and folded. The problem is that the shape is aligned at the edge of the page, and it cannot be expanded from a two-dimensional spread.

Although the idea of Patent Document 3 (Japanese Patent Application Laid-Open No. 2012-116656) is to provide a box that can be easily folded, the lid and bottom surfaces of the hexahedron structure are roughly the minimum unit for folding. Yes.

In the device of Patent Document 4 (Japanese Patent Application Laid-Open No. 2015-33772), it is for the problem that the design of the cylindrical folding structure part that becomes a curved cylindrical body is complicated. Was created, but it could only be created in a cylindrical shape.

Conventionally, as a protective cover, when the vehicle body is stored outdoors, it is soft like a cloth to protect the vehicle body from dust, mold, pollen, yellow sand, PM2.5 particles, rain water, or contamination by strong sunlight. A cover that covers the vehicle body composed of a seat is used. Among the protective covers, the protective cover for bicycles, motorcycles or tricycles has no large plane in the shape of the bicycle, motorcycle or tricycle, and is completely on the bicycles, motorcycles or tricycles. It was not possible to spread it, and it was normal to spread it while holding it in the hand and attach it to the car body, and it was necessary to make a judgment on the front, back, top and bottom, and left and right.

Although the protective cover of a car has a flat surface as a roof and can be spread on the roof, it is considerably larger than the protective cover of a bicycle, a motorcycle or a tricycle, so the front, back, top and bottom, and , Not only the left and right judgment, but the hand never reaches beyond the center of the car. I had to walk around the body, it was very cumbersome and the work was not easy.

Particularly common to all protective covers of the car body is that it is composed of a soft cloth-like sheet, although it has a fixed shape, so it can be used from the moment it is detached to the time the sheet is completely folded. The shape can be stored, and the detached shape is not stable. In other words, since there is a variation in the final shape that has been detached, even if it can be quickly detached, it has been necessary to eliminate the variation at the time of attachment.

Therefore, as a protective cover for a bicycle, a motorcycle or a tricycle, as disclosed in, for example, Utility Model Registration No. 3192626, a vertical slide fastener is attached to the side of the protective cover to smoothly attach and detach. There is a proposal, but there is no big plane in the shape of the bicycle, motorcycle or motorcycle, and it can not be fully extended on the bicycle, motorcycle or motorcycle, and it can be extended while holding it in the hand Therefore, it is usually mounted on the vehicle body, and it is necessary to judge the front / back, top / bottom and left / right, which is very troublesome and the work is not easy. In addition, since it is composed of a soft sheet such as cloth, it can be stored in any shape from the moment it is detached until the sheet is folded, and the detached shape is not stable.

Further, as disclosed in, for example, Japanese Patent Application Laid-Open No. 2004-67033, as a protective cover for an automobile, a protective cover that is wound around a winding plate is attached by rewinding and is removed by being wound. However, although the variation in the final shape has been eliminated, the protective cover itself is large, so it is necessary to walk around the vehicle body in order to wind it around. You have to walk around, it is very cumbersome and the work is not easy.

Furthermore, as a protective cover for a bicycle, a motorcycle, or a motorcycle, a three-dimensional shape with a loop-like elastic linear member is used as disclosed in, for example, Japanese Patent Application Laid-Open No. 2009-166730. Although what is held is proposed, although it is stored compactly by twisting the looped elastic linear material with a strong force and increasing the number of loops, it suddenly returns to its original shape, Although it is lightweight, when it grows in an unexpected direction, it feels quite heavy due to the lever principle and is difficult to handle. In addition, when it applies to the protective cover of a motor vehicle, it will become larger and handling will become more remarkable.

Japanese Patent Application No. 2013-17004 Japanese Patent Application No. 2007-154527 JP2012-116566A JP 2015-33772 A Utility Model Registration No. 3192626 JP 2004-67033 A JP 2009-166730 A

  The problem to be solved is that when folding a three-dimensional object etc. with a development view, it is not possible to decide how to fold, and there are many ways to fold, so it took time to fold or spread That is.

A further problem to be solved is that the protective cover is made of a soft sheet such as a cloth, so that the final shape after the protective cover is detached varies, and if a strong force is not applied, the attachment and removal are difficult. It is not easy.

The first of the present invention has a sheet,
The sheet has a plurality of regions divided by one or more boundary fold lines that are one or more fold lines forming a boundary;
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Of the two regions sandwiching each of the one or more boundary fold lines, one is a first region where the first fold line group intersects the boundary fold line, and the other is the second fold line. A group of lines is a second region intersecting the boundary fold line, and the first fold line group and the second fold line group intersecting the boundary fold line are the boundary fold line. The length of the line segment from the boundary fold line to the nearest intersection is between the first and second fold lines that are continuous with each other without branching. The second fold line is shorter than the first fold line,
When the boundary fold line extends in a straight line without bending at each intersection, the first and second fold lines that are continuous across the boundary fold line have the boundary fold line as the axis of symmetry. Intersect the boundary fold line at an angle that is line symmetric,
When the boundary fold line is bent with alternating positive and negative angles at each intersection, the first and second fold lines continuous across the boundary fold line are the boundary fold lines. Intersecting the boundary fold line at an angle that is a line symmetry axis of the boundary fold line that does not bend each other at the intersection with the line,
In each of the intersections of the first fold line group and the two second fold lines closest to the boundary fold line among the second fold line group in the first region, One and the other of the first fold lines sandwiching the intersection, and one and the other of the second fold lines sandwiching the intersection are the second fold with one of the first fold lines as an axis of symmetry. Line symmetry between a first imaginary line that is symmetric with respect to one of the lines and a second imaginary line that is symmetric with respect to one of the second fold lines with respect to the other of the first fold lines The axis corresponds to the other of the second fold lines,
Thereby, by folding along at least one of the one or more boundary fold lines, the sheet can be expanded in three dimensions, and all the surface elements in the sheet overlap each other, This is a folding structure that can fold a sheet.

The second of the present invention has a sheet,
The sheet is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
The group of first fold lines includes one or more linear first fold lines;
Thereby, the sheet can be expanded three-dimensionally by folding along at least one of the one or more linear first fold lines, and all the surface elements in the sheet are mutually connected. It is a foldable structure in which the sheets can be folded in an overlapping form.

The third of the present invention has a sheet,
The sheet has a plurality of regions divided by one or more boundary fold lines that are one or more fold lines forming a boundary;
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Of the two regions sandwiching each of the one or more boundary fold lines, one is a first region where the first fold line group intersects the boundary fold line, and the other is the second fold line. A group of lines is a second region intersecting the boundary fold line, and the first fold line group and the second fold line group intersecting the boundary fold line are the boundary fold line. The length of the line segment from the boundary fold line to the nearest intersection is between the first and second fold lines that are continuous with each other without branching. The second fold line is shorter than the first fold line,
When the boundary fold line extends in a straight line without bending at each intersection, the first and second fold lines that are continuous across the boundary fold line have the boundary fold line as the axis of symmetry. Intersect the boundary fold line at an angle that is line symmetric,
When the boundary fold line is bent with alternating positive and negative angles at each intersection, the first and second fold lines continuous across the boundary fold line are the boundary fold lines. Intersecting the boundary fold line at an angle that is a line symmetry axis of the boundary fold line that does not bend each other at the intersection with the line,
In each of the intersections of the first fold line group and the two second fold lines closest to the boundary fold line among the second fold line group in the first region, One and the other of the first fold lines sandwiching the intersection, and one and the other of the second fold lines sandwiching the intersection are the second fold with one of the first fold lines as an axis of symmetry. Line symmetry between a first imaginary line that is symmetric with respect to one of the lines and a second imaginary line that is symmetric with respect to one of the second fold lines with respect to the other of the first fold lines The axis corresponds to the other of the second fold lines,
In one or more of the plurality of regions, the group of first fold lines includes one or more linear first fold lines,
Thereby folding the sheet along at least one of the one or more boundary fold lines and at least one of the one or more linear first fold lines in the one or more regions. Is a foldable structure that allows the sheet to be folded in such a manner that all the surface elements in the sheet overlap each other.

The fourth of the present invention has a sheet,
The sheet has a plurality of regions cut along one or more lines and connected to each other by one or more connecting members in a belt-like and sheet-like manner that can bend and stretch.
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Thereby, by folding at least one of the one or more connecting members, the sheet can be expanded in three dimensions, and the sheet can be folded in a form in which all the surface elements in the sheet overlap each other. This is a folded structure.

According to a fifth aspect of the present invention, there is provided a folding structure according to any one of the first to fourth aspects, wherein the three-dimensional development is capable of forming five faces excluding one of the six faces of the hexahedron. .

A sixth aspect of the present invention is a folding structure according to the fifth aspect of the invention, which is a two-wheeled vehicle cover body.

A seventh aspect of the present invention is a folding structure according to the fifth aspect of the present invention, which is a car cover body.

According to an eighth aspect of the present invention, there is provided a folding structure according to any one of the first to fourth aspects, wherein the six-sided hexahedron can be formed as the three-dimensional development.

According to a ninth aspect of the present invention, in any one of the first to fourth aspects, the present invention is a folding structure that can form four surfaces of a tetrahedron as the three-dimensional development.

In the present invention, the sheet can be expanded in three dimensions means that the sheet can be expanded in three dimensions, not two dimensions, and is not limited to a tetrahedron, a hexahedron, etc. Also, a zigzag folded one or the like corresponds to a three-dimensionally developed one.

The effect of the present invention is to make a three-dimensional structure into a more compact shape by making a group of continuous fold lines that fold in the same direction into fold lines in a development view in a foldable structure that can fold a sheet. It is.

  Furthermore, the folding structure that can fold the sheet can be cantilevered when the crease remains because the group of continuous fold lines that fold in the same direction repeats positive and negative slopes alternately at the intersection. It is hard to crush.

Since it is a foldable structure that allows the sheet to be folded, it can be folded without being greatly unfolded, and it is not affected by the shape of the object to be protected.

Of the two regions divided by each of the boundary fold lines of the folding structure that can fold the sheet according to an embodiment of the present invention, one of the regions is alternately formed with positive and negative angles, A group of fold lines in which either one of the valley folds does not alternate with the other is an area where the boundary fold line intersects, and the other is a group of fold lines in which mountain folds and valley folds alternate at each intersection Is the area where the boundary fold line intersects, the center line of the group of fold lines that alternate between the positive and negative angles intersecting the boundary fold line, and the boundary fold line are perpendicular to each other. It is a perspective explanatory view of a foldable structure that can fold a sheet in which a fold line group in which a mountain fold and a valley fold alternate at each intersection that intersects a line, and a boundary fold line. FIG. 2 is a developed plan view of FIG. 1 according to an embodiment of the present invention. The boundary fold line in FIG. 2 according to an embodiment of the present invention is a fold line in which positive and negative angles are alternately formed, and either one of the mountain fold and the valley fold is not replaced with the other. FIG. Of the two regions divided by each of the boundary fold lines in FIG. 2 according to one embodiment of the present invention, one of them alternately forms an angle of positive and negative, and one of mountain fold and valley fold is A group of fold lines that are continuous without changing each other intersects the boundary fold line, and the other is a group of fold lines that alternate between mountain folds and valley folds at each intersection. It is an expansion plane explanatory drawing which extracted the circumference of a boundary fold line in the field to perform. FIG. 5 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape. FIG. 6 is a development plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape that is not shown in FIGS. 4 and 5. FIG. 7 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape that is not shown in FIGS. Of the two regions divided by each of the boundary fold lines of the folding structure that can fold the sheet according to an embodiment of the present invention, one of the regions is alternately formed with positive and negative angles, A group of fold lines in which either one of the valley folds does not alternate with the other is an area where the boundary fold line intersects, and the other is a group of fold lines in which mountain folds and valley folds alternate at each intersection Is the region that intersects the boundary fold line, and the center line of the group of fold lines that alternate between the positive and negative angles intersecting the boundary fold line is no longer perpendicular to the boundary fold line. It is a perspective explanatory view of a foldable structure that can fold a sheet in which a fold line where a mountain fold and a valley fold alternate at each intersection that intersects a line and a boundary fold line is not perpendicular. FIG. 9 is a developed plan view of FIG. 8 according to an embodiment of the present invention. Of the two regions divided by each of the boundary fold lines of the folding structure that can fold the sheet according to an embodiment of the present invention, one of the regions is alternately formed with positive and negative angles, A group of fold lines in which either one of the valley folds does not alternate with the other is an area where the boundary fold line intersects, and the other is a group of fold lines in which mountain folds and valley folds alternate at each intersection FIG. 5 is a perspective explanatory view of a folding structure that can fold a sheet that has an angle by assigning an angle to the area itself in an area that intersects the boundary fold line. FIG. 11 is a developed plan view of FIG. 10 according to an embodiment of the present invention. It is a perspective explanatory view of a foldable structure body that is a regular hexahedron shape made of a foldable structure body that can fold a sheet according to an embodiment of the present invention and that can fold a sheet. FIG. 13 is a developed plan view of FIG. 12 according to an embodiment of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a perspective explanatory view of a foldable structure having a regular tetrahedron shape created by a foldable structure that can fold a sheet according to an embodiment of the present invention, and that can fold a sheet. FIG. 15 is a developed plan view of FIG. 14 according to an embodiment of the present invention. Image development of a folding structure that can fold a sheet in five forms, in which a surface group constituting a solid according to an embodiment of the present invention is connected to two or less surface groups constituting another solid It is a top view. FIG. 2 is a perspective explanatory view showing a state in which a folding structure that can fold a seat, which is a cover body for a motorcycle according to an embodiment of the present invention, has been attached to a motorcycle. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory perspective view of a two-wheeled vehicle cover body according to an embodiment of the present invention, in which a folding structure that can fold a seat is attached to or detached from a motorcycle. A state in which the final fastening snap is not fastened before the folding structure, which is a motorcycle cover body according to an embodiment of the present invention, has been detachable from the motorcycle and becomes a storage shape. FIG. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory perspective view of a state in which a folding structure that can fold a seat, which is a motorcycle cover according to an embodiment of the present invention, is attached to a bicycle. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory perspective view of a state in which a folding structure that can fold a seat, which is a cover body for an automobile according to an embodiment of the present invention, is completely attached to an automobile.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.
FIG. 1 shows a folding structure that can fold a sheet according to an embodiment of the present invention, and one of the two regions divided by each of the boundary fold lines alternately has positive and negative angles. A group of fold lines in which one of mountain folds and valley folds does not alternate with the other is a region where the boundary fold line intersects, and the other is a mountain fold and a valley fold alternate at each intersection. In the region where the fold line group intersects the boundary fold line, the center line of the fold line group that alternates between the positive and negative angles intersecting the boundary fold line and the boundary fold line become perpendicular, In addition, a perspective explanatory view of a folding structure that can fold a group of fold lines in which mountain folds and valley folds alternate at each intersection that intersects the boundary fold line and a sheet in which the boundary fold line is perpendicular to each other. It is. FIG. 2 is a developed plan view of FIG. 3 is a development plane in which the boundary fold lines in FIG. 2 are alternately formed with positive and negative angles, and either one of the mountain folds or the valley folds is continuous without changing the other. FIG.
By alternating the positive and negative angles, if the angle at any intersection is an obtuse angle, the angle at the next intersection is an acute angle, and if the angle at any intersection is an acute angle, The angle at the next intersection is an obtuse angle. However, this does not apply if there is an inclination.
4 is one of the two regions divided by each of the boundary fold lines in FIG. 2, one of which alternately forms positive and negative angles, and either one of mountain fold or valley fold alternates with the other. A group of fold lines that are continuous without crossing the boundary fold line, and the other is a region where a group of fold lines where mountain folds and valley folds alternate at each intersection intersects with the boundary fold line. It is a development plane explanatory view which extracted a boundary fold line circumference fold line. FIG. 5 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created with a different shape. FIG. 6 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape that is not shown in FIGS. FIG. 7 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape that is not shown in FIGS. 4, 5, or 6. The reference numerals in FIGS. 4, 5, 6, and 7 indicate the number of steps in parentheses. The double broken line is a line projected with a symmetric line, and the angles with black circles are the same angle, and the angles with white circles are the same angle. In addition, a right angle is also shown. In other angle notations, only adjacent angles are the same angle.

  The double corrugated expandable structure, which is a folding structure that can fold the sheet, has a fold line that alternates between positive and negative angles, so that expansion and folding in the vertical and horizontal directions can be performed in parallel. However, it does not fully understand its operating principle. However, many models with the shapes shown in FIGS. 4, 5, 6, and 7 were made, and as a result of trial and error, regularity was discovered.

  The folding structure that can fold the sheet according to this embodiment includes intersections 1A, 2A, 3A, 4A, 5A, 5B, 5C, 5D, 5E, 4E, 3E, 2E, 1E, 1D, 1C, 1B, 1A. And a folding structure that can fold the sheet surrounded by 1 and 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, The folding structures that can fold the sheets surrounded by 1F and 1E are connected by a group of continuous straight folding lines connecting the intersections 1E, 2E, 3E, 4E, and 5E. In addition, as shown in FIG. 3, it can also connect by the group of the continuous folding line which connects the intersection 1M, 2M, 3M, 4M, 5M which makes the angle of positive and negative alternately at each intersection. The center line Za coincides with a group of continuous straight folding lines connecting the intersections 1E, 2E, 3E, 4E, and 5E. Further, the intersections where the reference numerals in FIG. 3 are not described are the same as those other than the intersections 1E, 2E, 3E, 4E, and 5E in FIG. Further, the fold line connecting the intersections 1E and 1F in FIG. 4 is the same fold line as the fold line X1 (1). Similarly, the fold line connecting the intersection points 1F and 1G and the fold line X2 (1), the fold line connecting the intersection points 1G and 1H and the fold line X3 (1), the fold line connecting the intersection points 1F and 2F and the fold line Y1 (1), The fold line connecting the intersection points 1G and 2G and the fold line Y2 (1), the fold line connecting the intersection points 2E and 2F and the fold line X1 (2), the fold line connecting the intersection points 2F and 2G and the fold line X2 (2), and the intersection point 2G Fold line connecting 2H and fold line X3 (2), fold line connecting intersection 2F and 3F and fold line Y1 (2), fold line connecting intersection 2G and 3G and fold line Y2 (2), fold connecting intersections 3E and 3F And fold line X1 (3), fold line and fold line X2 (3) connecting intersections 3F and 3G, fold line and fold line X3 (3) connecting intersections 3G and 3H, and fold line and fold connecting intersections 3F and 4F Line Y1 (3), fold line connecting intersections 3G and 4G, fold line Y2 (3), fold line connecting intersections 4E and 4F Fold line X1 (4), fold line connecting intersections 4F and 4G and fold line X2 (4), fold line connecting intersections 4G and 4H and fold line X3 (4), fold line connecting intersections 4F and 5F and fold line Y1 (4), the fold line connecting the intersections 4G and 5G and the fold line Y2 (4), the fold line connecting the intersections 5E and 5F and the fold line X1 (5), and the fold line connecting the intersections 5F and 5G and the fold line X2 (5) The fold line connecting the intersections 5G and 5H and the fold line X3 (5) are all the same fold line. The fold line X1 (1), the fold line X1 (1) 1, the fold line X1 (1) 2, and the fold line X1 (1) 3 in FIGS. 4, 5, 6, and 7 are lengths and angles. Although they are different, their roles in the related positions and surface elements are the same. Similarly, fold line X1 (2), fold line X1 (2) 1, fold line X1 (2) 2, fold line X1 (2) 3, fold line X1 (3), fold line X1 (3) 1, Fold line X1 (3) 2, Fold line X1 (3) 3, Fold line X1 (4), Fold line X1 (4) 1, Fold line X1 (4) 2, Fold line X1 (4) 3, Fold Line X1 (5), fold line X1 (5) 1, fold line X1 (5) 2, fold line X1 (5) 3, fold line X2 (1), fold line X2 (1) 1, fold line X2 ( 1) 2, fold line X2 (1) 3, fold line X2 (2), fold line X2 (2) 1, fold line X2 (2) 2, fold line X2 (2) 3, and fold line X2 (3 ), Fold line X2 (3) 1, fold line X2 (3) 2, fold line X2 (3) 3, fold line X2 (4), fold line X2 (4) 1, fold line X2 (4) 2, Fold line X2 (4) 3, fold line X2 (5), Fold line X2 (5) 1, fold line X2 (5) 2, fold line X2 (5) 3, fold line X3 (1), fold line X3 (1) 1, fold line X3 (1) 2, fold line X3 (1) 3, fold line X3 (2), fold line X3 (2) 1, fold line X3 (2) 2, fold line X3 (2) 3, fold line X3 (3), fold line X3 ( 3) 1, fold line X3 (3) 2, fold line X3 (3) 3, fold line X3 (4), fold line X3 (4) 1, fold line X3 (4) 2, fold line X3 (4) 3, fold line X3 (5), fold line X3 (5) 1, fold line X3 (5) 2, fold line X3 (5) 3, fold line Y1 (1), fold line Y1 (1) 1, Fold line Y1 (1) 2, Fold line Y1 (1) 3, Fold line Y1 (2), Fold line Y1 (2) 1, Fold line Y1 (2) 2, Fold line Y1 (2) 3, Fold Line Y1 (3), fold line Y1 (3) 1, fold line 1 (3) 2, fold line Y1 (3) 3, fold line Y1 (4), fold line Y1 (4) 1, fold line Y1 (4) 2, fold line Y1 (4) 3, and fold line Y2 (1), fold line Y2 (1) 1, fold line Y2 (1) 2, fold line Y2 (1) 3, fold line Y2 (2), fold line Y2 (2) 1, and fold line Y2 (2) 2, fold line Y2 (2) 3, fold line Y2 (3), fold line Y2 (3) 1, fold line Y2 (3) 2, fold line Y2 (3) 3, fold line Y2 (4), Although the fold line Y2 (4) 1, the fold line Y2 (4) 2, and the fold line Y2 (4) 3 are different in length and angle, they play the same role in related positions and surface elements.

There are valley folds and mountain folds, and the valley fold is a way to fold the surface and the surface together so that they are recessed, like a valley, and the mountain fold is the back and back It is a way to fold it up like a mountain. If the front and back are turned over, the valley fold becomes a mountain fold, and the mountain fold becomes a valley fold.
The folding method in this explanatory diagram is based on a group of continuous folding lines connecting the intersection points 1B, 2B, 3B, 4B, and 5B, and the intersection points 1D, 2D, and 3D. A group of continuous fold lines connecting 4D and 5D and a group of continuous fold lines connecting intersections 2E, 2F, 2G, 2H, 2J, and 2K and intersection points 4E, 4F, 4G, 4H, 4J, and 4K are connected. A group of continuous folding lines becomes a continuous mountain fold,
A group of continuous folding lines connecting the intersection points 1C, 2C, 3C, 4C, and 5C, and alternating points 3E, 3F, 3G, 3H, 3J, and 3K, which are alternately positive and negative at each intersection. A group of folding lines and a group of continuous folding lines connecting the straight intersections 1E, 2E, 3E, 4E, and 5E form a continuous valley fold.
Non-continuous mountain folds are a fold line connecting intersections 2A and 2B, a fold line connecting intersections 2C and 2D, a fold line connecting intersections 3B and 3C, a fold line connecting intersections 3D and 3E, and a fold line connecting intersections 4A and 4B , A fold line connecting the intersection points 4C and 4D, a fold line connecting the intersection points 1F and 2F, a fold line connecting the intersection points 1H and 2H, a fold line connecting the intersection points 2G and 3G, a fold line connecting the intersection points 2J and 3J, and the intersection points 3F and 4F A fold line connecting the intersection points 3H and 4H, a fold line connecting the intersection points 4G and 5G, and a fold line connecting the intersection points 4J and 5J.
Discontinuous valley folds are a fold line connecting intersections 2B and 2C, a fold line connecting intersections 2D and 2E, a fold line connecting intersections 3A and 3B, a fold line connecting intersections 3C and 3D, and a fold line connecting intersections 4B and 4C. , A fold line connecting the intersection points 4D and 4E, a fold line connecting the intersection points 1G and 2G, a fold line connecting the intersection points 1J and 2J, a fold line connecting the intersection points 2F and 3F, a fold line connecting the intersection points 2H and 3H, and an intersection point 3G and 4G , A fold line connecting the intersection points 3J and 4J, a fold line connecting the intersection points 4F and 5F, and a fold line connecting the intersection points 4H and 5H.
Folding structure that can fold the sheet if all folding lines are changed to valley folds for mountain folds and mountain folds for valley folds if one fold line is folded. Does not hold, that is, there are only two ways to fold the folding structure that can fold the sheet.

There is a certain regularity in the folding method of the folding structure that enables the sheet to be folded, and in the folding method in which a group of folding lines is continuous, positive and negative angles are alternately formed at each intersection. When the group of continuous folding lines connecting the intersection points 1B, 2B, 3B, 4B, 5B is a mountain fold, the intersection points 1C, 2C, 3C, 4C, 5C are alternately formed at positive and negative angles at each intersection point. So that the group of continuous fold lines connecting
When the group of continuous fold lines connecting the intersection points 1C, 2C, 3C, 4C, and 5C is a valley fold, the angles between positive and negative are alternately valley-folded at each intersection. A group of continuous fold lines connecting the intersection points 1D, 2D, 3D, 4D, and 5D into mountain folds.
In addition, when the group of continuous folding lines connecting the intersections 2E, 2F, 2G, 2H, 2J, and 2K that are alternately positive and negative at each intersection is a mountain fold, positive and negative at each intersection A group of continuous fold lines connecting the intersections 3E, 3F, 3G, 3H, 3J, and 3K, which make an angle with the negative, are valley folds,
If the group of continuous fold lines connecting the intersections 3E, 3F, 3G, 3H, 3J, and 3K that are alternately positive and negative at each intersection is a valley fold, positive and negative at each intersection The group of continuous fold lines connecting the intersections 4E, 4F, 4G, 4H, 4J, and 4K, which are alternately angled, are mountain-folded.
A group of continuous folding lines is the same folding method and is not arranged in an adjacent row.
In a group of folding lines in which folding is not continuous, if the folding line connecting the intersections 2B and 2C is a valley fold, the folding line connecting the intersections 2B and 1B, the folding line connecting the intersections 2B and 2A, the intersection 2B And the fold line connecting 3B becomes a mountain fold,
If the fold line connecting the intersections 2D and 2E is a valley fold, the fold line connecting the intersections 2D and 1D, the fold line connecting the intersections 2D and 2A, and the fold line connecting the intersections 2D and 3D are mountain folds.
In the column next to the group of folding lines where the folding is not continuous, the direction is reversed, and the folding line connecting the intersections 3B and 3A is a valley fold, the folding line connecting the intersections 3B and 2B, the intersection The fold line connecting 3B and 3C and the fold line connecting intersections 3B and 4B are mountain folds,
If the fold line connecting the intersection points 3D and 3C is a valley fold, the fold line connecting the intersection points 3D and 2D, the fold line connecting the intersection points 3D and 3E, and the fold line connecting the intersection points 3D and 4D are mountain folds.
In the next row of the group of folding lines where the folding is not continuous, the direction returns to the original, and the folding line connecting the intersections 4B and 4E is valley folding, the folding line connecting the intersections 4B and 3B on the top, bottom, left and right, The fold line connecting the intersection points 4B and 4C and the fold line connecting the intersection points 4B and 5B are mountain folds,
If the fold line connecting the intersection points 4D and 4E is a valley fold, the fold line connecting the intersection points 4D and 3D, the fold line connecting the intersection points 4D and 4A, and the fold line connecting the intersection points 4D and 5D are mountain folds. like,
Similarly, in a group of folding lines in which folding is not continuous, if the folding line connecting the intersections 2J and 1J is a valley fold, the folding line connecting the intersections 2J and 2K, the folding line connecting the intersections 2J and 3J, up, down, left and right The fold line connecting the intersections 2J and 2H is a mountain fold,
If the fold line connecting the intersections 4J and 3J is a valley fold, the fold line connecting the intersections 4J and 4K, the fold line connecting the intersections 4J and 5J, and the fold line connecting the intersections 4J and 4H are mountain folds.
In the column next to the group of folding lines where the folding is not continuous, the direction is reversed, and the folding line connecting the intersections 2H and 3H is valley folding, the folding line connecting the intersections 2H and 2J, the intersection A fold line connecting 2H and 1H and a fold line connecting intersections 2H and 2G are mountain folds,
If the fold line connecting the intersections 4H and 5H is a valley fold, the fold line connecting the intersections 4H and 4J, the fold line connecting the intersections 4H and 3H, and the fold line connecting the intersections 4H and 4G are mountain folds.
In the next row of the group of folding lines where the folding is not continuous, the direction returns to the original, and the folding line connecting the intersections 2G and 1G is valley folding, the folding line connecting the intersections 2G and 2H on the top, bottom, left and right, The fold line connecting the intersections 2G and 3G and the fold line connecting the intersections 2G and 2F are mountain folds,
If the fold line connecting the intersections 4G and 3G is a valley fold, the fold line connecting the intersections 4G and 4H, the fold line connecting the intersections 4G and 5G, and the fold line connecting the intersections 4G and 4F are mountain folds.
In the next row of the group of folding lines where the folding is not continuous, the direction is reversed, and if the folding line connecting the intersections 2F and 3F is a valley fold, the folding connecting the intersections 2F and 2G on the top, bottom, left and right Line, fold line connecting intersections 2F and 1F, fold line connecting intersections 2F and 2E are mountain folds,
If the fold line connecting the intersection points 4F and 5F is a valley fold, the fold line connecting the intersection points 4F and 4G, the fold line connecting the intersection points 4F and 3F, and the fold line connecting the intersection points 4F and 4E are mountain folds. like,
Mountain folds and valley folds are staggered.
In other words, the folding method created from a certain regularity has a positive and negative angle at the intersection, and the direction in which the fold line is continuously connected by valley folds or mountain folds, and the positive and negative angles at the intersection. It can be seen that the fold line intersects with a group of fold lines that are continuously connected by valley folds or mountain folds while being given, and there is a direction in which valley folds and mountain folds are connected while being switched for each fold line.

Originally, the double corrugated expandable structure that applied the expandable surface has a structure that can be folded and unfolded just by pushing and pulling it once, having two surface elements in the diagonal part, Since folding lines having different directivities are connected by matching the number of intersections, they cannot be folded once. However, it can be folded by adding a procedure.
That is, even if the surface element surrounded by the intersection points 1J, 2J, 2K, 1K, and 1J and the surface element and the back surface of the surface element surrounded by the intersection points 4A, 5A, 5B, 4B, and 4A are pinched with fingers, the distance is reduced. Can't fold.
Therefore, when the distance between the intersection points 4A, 5A, 5B, 4B, and 4A and the surface elements surrounded by the intersection points 1D, 2D, 2E, 1E, and 1D is reduced by a finger and the distance is reduced, the intersection points 1A, 2A, 3A 4A, 5A, 5B, 5C, 5D, 5E, 4E, 3E, 2E, 1E, 1D, 1C, 1B, 1A, the folding structure that can be folded is folded,
The surface element group surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 4F, 3F, 2F, 1F, and 1E is also folded.
Further, the surface element group surrounded by the intersection points 1F, 2F, 3F, 4F, 5F, 5G, 4G, 3G, 2G, 1G, and 1F is slightly folded.
After that, the sheet surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, and 1E can be folded. Because part of the folded structure is folded and the folds become clear,
Fully folded sheet 1A, 2A, 3A, 4A, 5A, 5B, 5C, 5D, 5E, 4E, 3E, 2E, 1E, 1D, 1C, 1B, 1A can be folded. It can be folded by pinching the folded structure with your fingers and shrinking the whole with the opposite palm.
Strictly speaking, when expanding, the procedure is reversed, but since the force is released, it can be expanded with a sense of pulling only once.

Note that the folding procedure occurs because a folding structure that allows two sheets to be folded in different directions is connected, so the folding structure that allows one sheet to be folded is limited by the boundary. This is because it has occurred.
Specifically, at each intersection, a group of continuous folding lines connecting the intersections 1B, 2B, 3B, 4B, and 5B that alternately make positive and negative angles have three directions at the intersection 1B and the intersection 5B. There are no restrictions because only two fold lines are connected, and two of them hit the edges.
At each intersection point, a group of continuous fold lines connecting the intersection points 1C, 2C, 3C, 4C, and 5C, alternately forming positive and negative angles, the intersection point 1C and the intersection point 5C are also connected in only three fold lines. There are no restrictions because two of them hit the edges.
At each intersection point, a group of continuous fold lines connecting the intersection points 1D, 2D, 3D, 4D, and 5D, alternately forming positive and negative angles, the intersection point 1D and the intersection point 5D are also connected in only three directions. There are no restrictions because two of them hit the edges.
Only three fold lines are connected to the intersection points 1E and 5E of the group of continuous folding lines connecting the intersection points 1E, 2E, 3E, 4E, and 5E, and two of them are edges. Because there is no restriction,
At the intersections 2E, 2F, 2G, 2H, 2J, 2K, which are alternately positive and negative angles, the intersection 2E of the group of continuous folding lines connecting the intersections 2D and 2E in the opposite folding manner. Since there is a continuous fold line connecting the two, there is a restriction that cannot be folded only by a group of continuous fold lines connecting the intersections 2E, 2F, 2G, 2H, 2J, and 2K.
The intersections 3D and 3E of the reverse folding method are also applied to the intersection 3E of the group of continuous folding lines connecting the intersections 3E, 3F, 3G, 3H, 3J, and 3K, which are alternately positive and negative at each intersection. Since there is a continuous fold line connecting the two, there is a restriction that cannot be folded only by a group of continuous fold lines connecting the intersections 3E, 3F, 3G, 3H, 3J, 3K.
The intersections 4D and 4E of the reverse folding method are also applied to the intersection 4E of the group of continuous folding lines connecting the intersections 4E, 4F, 4G, 4H, 4J, and 4K, which are alternately positive and negative at each intersection. This is because there are restrictions that cannot be folded only by a group of continuous folding lines connecting the intersections 4E, 4F, 4G, 4H, 4J, and 4K.

As another constraint, the sheet surrounded by the intersections 1A, 2A, 3A, 4A, 5A, 5B, 5C, 5D, 5E, 4E, 3E, 2E, 1E, 1D, 1C, 1B, 1A can be folded. The folding structure is
A group of continuous fold lines connecting the intersection points 1B, 2B, 3B, 4B, 5B, which are alternately positive and negative at each intersection point, are mountain folds,
A group of continuous fold lines connecting the intersections 1C, 2C, 3C, 4C, and 5C are valley folds, and a group of continuous fold lines connecting the intersections 1D, 2D, 3D, 4D, and 5D are mountain folds,
When a group of continuous fold lines connecting straight intersections 1E, 2E, 3E, 4E, 5E is folded in a valley fold,
Since it is folded on the surface element group surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 4F, 3F, 2F, 1F, 1E, the intersection points 1E and 1F are defined by the fold line connecting the intersection points 1D and 1E. The length of the connecting fold line is made longer, the length of the fold line connecting the intersection points 2E and 2F is made longer than the fold line connecting the intersection points 2D and 2E, and the intersection point 3E and the fold line connecting the intersection points 3D and 3E Make the length of the fold line connecting 3F longer, make the length of the fold line connecting intersections 4E and 4F longer than the fold line connecting intersections 4D and 4E, and make the intersection point more than the fold line connecting intersections 5D and 5E The length of the fold line connecting 5E and 5F is made longer to prevent interference.
Of course, by alternating the positive and negative angles at each intersection, the fold lines that enter the interior, specifically the intersections 1B and 1C, are escaped from interference or bulge due to thickness. It is also important that the fold line connecting the intersection points 2B and 2C, the fold line connecting the intersection points 3B and 3C, the fold line connecting the intersection points 4B and 4C, and the fold line connecting the intersection points 5B and 5C are not extremely long. .
Although it is not a limitation, since thickness is not considered in paper or the like, considering thickness, a fold line connecting intersections 1E and 1F, a fold line connecting intersections 1E and 1F, a fold line connecting intersections 1E and 1F, and an intersection It is also necessary to increase the length of the fold line connecting 1E and 1F and the fold line connecting intersections 1E and 1F.

For a boundary part where two folding structures having different directions are connected, when a group of continuous straight fold lines connecting the intersections 1E, 2E, 3E, 4E, and 5E are folded at a valley fold, A group of continuous fold lines connecting 1E, 2E, 3E, 4E, and 5E is a straight line, and the fold line connecting intersections 1D and 1E is a fold line connecting intersections 1E and 1F, with the group of fold lines as a symmetric line. The fold line connecting the intersection points 2D and 2E is the fold line connecting the intersection points 2E and 2F, the fold line connecting the intersection points 3D and 3E is the fold line connecting the intersection points 3E and 3F, and the fold line connecting the intersection points 4D and 4E is the intersection point 4E. 4F and the fold line connecting the intersections 5D and 5E overlap the fold line connecting the intersections 5E and 5F. In this case, since the group of fold lines at the boundary portion can be made linear, the shape after unfolding can be seen beautifully, but it is difficult to fold and has the disadvantage that it can be either valley fold or mountain fold.
In the folding structure as shown in FIG. 3, a group of fold lines connecting the intersections 2D, 2M, and 2F is linear, and a fold line connecting the intersections 1M and 2M is defined as a symmetric line with the group of fold lines being the intersections 2M and 3M. A fold line connecting the intersection points 3D, 3M, and 3F is a straight line, and the fold line connecting the intersection points 2M and 3M is a fold line connecting the intersection points 3M and 4M. The group of folding lines connecting the intersections 4D, 4M, and 4F is linear, and the folding line connecting the intersections 3M and 4M overlaps the folding line connecting the intersections 4M and 5M. . In this case, since the group of fold lines at the connecting portion cannot be made linear, the shape after unfolding cannot be shown beautifully. On the other hand, it is easy to fold, and in the case of mountain folds, it is difficult to fold the valleys. In this case, it becomes difficult to fold the valley and the folding direction is stabilized.

Folding structure that can fold a sheet surrounded by intersections 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, 1E The body part will be described in more detail.
A fold line connecting the intersection points 1J and 1H and an intersection point 1J and 1K in a group of continuous fold lines connecting the intersection points 1E, 1F, 1G, 1H, 1J, and 1K, with positive and negative angles alternately at each intersection. The angle formed by the fold line connecting the intersections 1H and 1G is opposite to the angle formed by the fold line connecting the intersections 1H and 1G (fold line X3 (1)) and the angle formed by the fold line connecting the intersections 1H and 1J. A fold line connecting the intersections 2J and 2H and a fold line connecting the intersections 2J and 2K are formed of a group of continuous fold lines connecting the intersections 2E, 2F, 2G, 2H, 2J, and 2K, which form an angle with the negative. Opposite angles, but the angle formed by the fold line connecting the intersections 2H and 2G (fold line X3 (2)) and the fold line connecting the intersections 2H and 2J, and the positive and negative angles alternately at each intersection The intersection 3J of the group of continuous folding lines connecting the intersections 3E, 3F, 3G, 3H, 3J, 3K Although the fold line connecting H and the fold line connecting the intersections 3J and 3K are opposite, the fold line connecting the intersections 3H and 3G (fold line X3 (3)) and the fold line connecting the intersections 3H and 3J is A fold line connecting the intersection points 4J and 4H of a group of continuous fold lines connecting the intersection points 4E, 4F, 4G, 4H, 4J, and 4K, alternately forming positive and negative angles at each intersection point The angle formed by the fold line connecting the intersection points 4J and 4K is opposite to the angle formed by the fold line connecting the intersection points 4H and 4G (fold line X3 (4)) and the fold line connecting the intersection points 4H and 4J, and each intersection point. Then, the fold line connecting the intersection points 5J and 5H and the intersection points 5J and 5K in the group of continuous fold lines connecting the intersection points 5E, 5F, 5G, 5H, 5J, and 5K, which are alternately positive and negative, are connected. Although it is opposite to the angle formed by the fold line, the fold line connecting the intersections 5H and 5G (fold line X3 ( )) And the intersection 5H and angle fold lines make connecting 5 J, all despite the same angle,
A fold line (fold line X3 () that connects the intersection points 1G and 1H in a group of continuous fold lines that connect the intersection points 1E, 1F, 1G, 1H, 1J, and 1K, which are alternately positive and negative at each intersection point. 1)) and the fold line connecting the intersection points 1G and 1F (fold line X2 (1)) is opposite, but the fold line connecting the intersection points 1F and 1G (fold line X2 (1)) and the intersection point 1F The fold line connecting the intersections 2E, 2F, 2G, 2H, 2J, and 2K, in which the angle formed by the fold line (fold line X1 (1)) connecting 1E and the positive and negative angles are alternated at each intersection In the group of lines, the angle formed by the fold line connecting the intersection points 2G and 2H (fold line X3 (2)) and the fold line connecting the intersection points 2G and 2F (fold line X2 (2)) is opposite to the intersection point 2F. A fold line (fold line X2 (2)) connecting 2G and 2G and a corner formed by a fold line (fold line X1 (2)) connecting intersections 2F and 2E And a fold line (fold line) connecting the intersection points 3G and 3H of a group of continuous fold lines connecting the intersection points 3E, 3F, 3G, 3H, 3J, and 3K, which alternately form positive and negative angles at each intersection point. X3 (3)) and the angle formed by the fold line (fold line X2 (3)) connecting the intersection points 3G and 3F is opposite to the angle formed by the fold line (fold line X2 (3)) connecting the intersection points 3F and 3G. Continuation connecting the intersections 4E, 4F, 4G, 4H, 4J, and 4K, in which the angle formed by the fold line connecting the 3F and 3E (fold line X1 (3)) and the positive and negative angles are alternated at each intersection The angle between the fold line connecting the intersection points 4G and 4H (fold line X3 (4)) and the fold line connecting the intersection points 4G and 4F (fold line X2 (4)) of the group of folding lines to be formed is opposite, A fold line connecting the intersection points 4F and 4G (fold line X2 (4)) and a fold line connecting the intersection points 4F and 4E (fold line X1 (4)) are present. And a fold line connecting the intersection points 5G and 5H in a group of continuous fold lines connecting the intersection points 5E, 5F, 5G, 5H, 5J, and 5K, which are alternately positive and negative angles at each intersection point ( The fold line connecting the intersection points 5F and 5G (fold line X2 (5)) is opposite to the angle formed by the fold line (fold line X2 (5)) connecting the fold line X3 (5)) and the intersection points 5G and 5F. And the angle formed by the fold line (fold line X1 (5)) connecting the intersections 5F and 5E are all different angles.
In addition, a group of continuous fold lines connecting the intersections 1H, 2H, 3H, 4H, and 5H and a group of continuous fold lines connecting the intersections 1J, 2J, 3J, 4J, and 5J are linear fold lines. A fold line connecting intersection points 2F and 1F in a group of continuous fold lines connecting intersection points 1F, 2F, 3F, 4F, and 5F that alternately form positive and negative angles at each intersection point regardless of the group ( The angle formed by the fold line (fold line Y1 (2)) connecting the fold line Y1 (1)) and the intersection points 2F and 3F, and the fold line (fold line Y1 (3)) connecting the intersection points 4F and 3F and the intersection points 4F and 5F The fold line connecting the intersections 3F and 2F (fold line Y1 (2)) and the fold line connecting the intersections 3F and 4F (fold line) is opposite to the angle formed by the fold line connecting the intersections (fold line Y1 (4)). Y1 (3)) and the intersection points 1G, 2G, 3G, which alternately make positive and negative angles at each intersection point, The angle formed by the fold line connecting the intersections 2G and 1G (fold line Y2 (1)) and the fold line connecting the intersections 2G and 3G (fold line Y2 (2)) of the group of continuous fold lines connecting G and 5G The angle between the fold line connecting the intersection points 4G and 3G (fold line Y2 (3)) and the fold line connecting the intersection points 4G and 5G (fold line Y2 (4)) is opposite, but connects the intersection points 3G and 2G. The angles formed by the fold line (fold line Y2 (3)) connecting the fold line (fold line Y2 (2)) and the intersections 3G and 4G are all different angles.
The reason for this is that a group of fold lines with directional and alternating positive and negative angles at each intersection is an indispensable element for a fold structure, and two fold structures with different directions are When connecting at an intended angle or at an intended position, it has a group of fold lines at the boundary of the foldable structure that allows the sheet to be folded on the side that is not the foldable structure that allows the sheet to be folded first. A fold line of the first surface element group extending in one row, the second surface element group adjacent to the first surface element group, and the third surface element group adjacent to the second surface element group This is thought to be for connecting to the intended angle or intended position by changing the length or angle of the.
Specifically, the sheet originally surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, 1E The folding structure that can be folded is a continuous line connecting the intersection points 1F, 2F, 3F, 4F, and 5F unless connected by a group of continuous straight fold lines that connect the intersection points 1E, 2E, 3E, 4E, and 5E. The fold line group and the continuous fold line group connecting the intersection points 1G, 2G, 3G, 4G, and 5G are linear, and a fold line connecting the intersection points 2G and 2F and a fold line connecting the intersection points 2G and 2H are formed. The angle is equal to the angle formed by the fold line connecting the intersections 2J and 2H and the fold line connecting the intersections 2J and 2K, and the angle formed by the fold line connecting the intersections 2F and 2E and the fold line connecting the intersections 2F and 2G is At the fold line connecting 2H and 2G and the intersection 2H and 2J Folding structure surrounded by intersections 1A, 2A, 3A, 4A, 5A, 5B, 5C, 5D, 5E, 4E, 3E, 2E, 1E, 1D, 1C, 1B, 1A The position is different from the position of the intersection point 2E when the body is connected, and the same applies to the intersection point 3E and the intersection point 4E, and it is considered that the length and angle of the folding line are changed for the correction.
The angle formed by the fold line (fold line Y1 (1)) connecting the intersection points 2F and 1F and the fold line connecting the intersection points 2F and 3F (fold line Y1 (2)), the fold line connecting the intersection points 2G and 1G (fold line Y2 ( 1)) and an angle formed by a fold line (fold line Y2 (2)) connecting the intersection points 2G and 3G, a fold line connecting the intersection points 3F and 2F (fold line Y1 (2)) and a fold line connecting the intersection points 3F and 4F ( The angle formed by the fold line Y1 (3)), the angle formed by the fold line connecting the intersections 3G and 2G (fold line Y2 (2)) and the fold line connecting the intersections 3G and 4G (fold line Y2 (3)), and the intersection 4F Is the angle formed by the fold line (fold line Y1 (3)) connected by 3F and the fold line (fold line Y1 (4)) connected by intersections 4F and 5F, and the fold line (fold line Y2 (3) connected by intersections 4G and 3G) ) And the angle formed by the fold line (fold line Y2 (4)) connecting the intersection points 4G and 5G, the fold line connecting the intersection points 1F and 1E (fold line) An angle formed by a fold line (fold line X2 (1)) connecting line X1 (1)) and intersections 1F and 1G, and a fold line (fold line X2 (1)) connecting intersections 1G and 1F and intersections 1G and 1H. The angle formed by the fold line (fold line X3 (1)), the fold line connecting the intersections 2F and 2E (fold line X1 (2)) and the fold line connecting the intersections 2F and 2G (fold line X2 (2)) The angle formed by the fold line connecting the intersections 2G and 2F (fold line X2 (2)) and the fold line connecting the intersections 2G and 2H (fold line X3 (2)), and the fold line connecting the intersections 3F and 3E (fold line X1) (3)) and an angle formed by a fold line (fold line X2 (3)) connecting the intersection points 3F and 3G, a fold line connecting the intersection points 3G and 3F (fold line X2 (3)) and a fold line connecting the intersection points 3G and 3H The angle formed by (fold line X3 (3)), the fold line connecting the intersection points 4F and 4E (fold line X1 (4)) and the intersection points 4F and 4 The fold line (fold line X2 (4)) formed by the fold line, the fold line (fold line X2 (4)) connecting the intersection points 4G and 4F (fold line X3 (4)) and the fold line connecting the intersection points 4G and 4H (fold line X3 (4)) The angle formed by the fold line connecting the intersections 5F and 5E (fold line X1 (5)) and the fold line connecting the intersections 5F and 5G (fold line X2 (5)) and the fold line connecting the intersections 5G and 5F (fold) The angle formed by the fold line (fold line X3 (5)) connecting the line X2 (5)) and the intersections 5G and 5H is considered by comparing FIGS. 5, 6, and 7, and the fold line Y1 ( 1) Angle formed by 1 and fold line Y1 (2) 1, angle formed by fold line Y2 (1) 1 and fold line Y2 (2) 1, fold line Y1 (2) 1 and fold line Y1 (3) 1 The angle formed by the fold line Y2 (2) 1 and the fold line Y2 (3) 1, the angle formed by the fold line Y1 (3) 1 and the fold line Y1 (4) 1, the fold line Angle formed by Y2 (3) 1 and fold line Y2 (4) 1, angle formed by fold line X1 (1) 1 and fold line X2 (1) 1, fold line X2 (1) 1 and fold line X3 (1) 1, the angle formed by the fold line X1 (2) 1 and the fold line X2 (2) 1, the angle formed by the fold line X2 (2) 1 and the fold line X3 (2) 1, the fold line X1 (3) 1 And the angle formed by the fold line X2 (3) 1, the angle formed by the fold line X2 (3) 1 and the fold line X3 (3) 1, the angle formed by the fold line X1 (4) 1 and the fold line X2 (4) 1, Angle formed by fold line X2 (4) 1 and fold line X3 (4) 1, angle formed by fold line X1 (5) 1 and fold line X2 (5) 1, fold line X2 (5) 1 and fold line X3 ( 5) The angle formed by 1 is considered while comparing FIG. 4, FIG. 6, and FIG. 7. The angle formed by the fold line Y1 (1) 2 and the fold line Y1 (2) 2 in FIG. ) Fold with 2 Angle formed by Y2 (2) 2, angle formed by fold line Y1 (2) 2 and fold line Y1 (3) 2, angle formed by fold line Y2 (2) 2 and fold line Y2 (3) 2, fold line Y1 (3) Angle formed by 2 and fold line Y1 (4) 2, angle formed by fold line Y2 (3) 2 and fold line Y2 (4) 2, fold line X1 (1) 2 and fold line X2 (1) 2 , The angle formed by the fold line X2 (1) 2 and the fold line X3 (1) 2, the angle formed by the fold line X1 (2) 2 and the fold line X2 (2) 2, and the fold line X2 (2) 2. Angle formed by fold line X3 (2) 2, angle formed by fold line X1 (3) 2 and fold line X2 (3) 2, angle formed by fold line X2 (3) 2 and fold line X3 (3) 2, The angle formed by the line X1 (4) 2 and the fold line X2 (4) 2, the angle formed by the fold line X2 (4) 2 and the fold line X3 (4) 2, the fold line X1 (5) 2 and the fold line X2 (5 2) The angle formed by the folding line X2 (5) 2 and the folding line X3 (5) 2 is considered while comparing FIG. 4, FIG. 5, and FIG. 7, and the folding line Y1 (1) 3 in FIG. Angle formed by line Y1 (2) 3, angle formed by fold line Y2 (1) 3 and fold line Y2 (2) 3, angle formed by fold line Y1 (2) 3 and fold line Y1 (3) 3, fold line Angle formed by Y2 (2) 3 and fold line Y2 (3) 3, angle formed by fold line Y1 (3) 3 and fold line Y1 (4) 3, fold line Y2 (3) 3 and fold line Y2 (4) 3, the angle formed by the fold line X 1 (1) 3 and the fold line X 2 (1) 3, the angle formed by the fold line X 2 (1) 3 and the fold line X 3 (1) 3, and the fold line X 1 (2) 3 And the angle formed by the fold line X2 (2) 3, the angle formed by the fold line X2 (2) 3 and the fold line X3 (2) 3, the angle formed by the fold line X1 (3) 3 and the fold line X2 (3) 3, Fold line X2 (3) Angle formed by 3 and fold line X3 (3) 3, angle formed by fold line X1 (4) 3 and fold line X2 (4) 3, fold line X2 (4) 3 and fold line X3 (4) 3 , The fold line X1 (5) 3 and the fold line X2 (5) 3, and the fold line X2 (5) 3 and the fold line X3 (5) 3. Considering 6 by comparing, the angle of each inclination is not significant, and the regularity that the inclination gives to other inclinations can be found.
That is, the sheet surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, and 1E can be folded. Fold the sheet surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, 1E. The foldable structure portion made possible is considered to be a deformation region with regularity for correcting the position and angle.

I will explain the regularity in the deformation area.
Although the same applies to any stage, the second stage will be specifically described as an example.
In the second stage, there are three surface element groups: a surface element surrounded by intersections 2E, 3E, 3F, 2F, and 2E; a surface element surrounded by intersections 2F, 3F, 3G, 2G, and 2F; In the case of a plane element surrounded by 2G, 3G, 3H, 2H, and 2G, there are two groups of three fold lines that are continuously connected by valley folds or mountain folds at intersections 2E, 2F, and 2G. There are a group of fold lines connecting 2H and a group of fold lines connecting intersections 3E, 3F, 3G and 3H. If we consider a group of fold lines connecting intersections 2E, 2F, 2G and 2H, A fold line connecting 2E (fold line X1 (2)) is a symmetric line, an intersection 2F is a starting point, a fold line connecting the intersections 2F and 3F (fold line Y1 (2)), and an intersection 2F and 2G A fold line connecting the two lines (fold line X2 (2)) is a symmetric line, the intersection point 2F is the starting point, and the intersection point 2F The bisector of the fold line connecting 3F (fold line Y1 (2)) is the fold line connecting the intersections 2F and 1F (fold line Y1 (1)) and the fold connecting the intersections 2G and 2F A fold line connecting the intersections 2G and 2H, and a fold line connecting the intersections 2G and 3G (fold line Y2 (2)) with the line (fold line X2 (2)) as the symmetric line and the intersection 2G as the starting point The bisector of the fold line (fold line Y2 (2)) connecting the intersection points 2G and 3G with the (fold line X3 (2)) as the symmetry line and the intersection point 2G as the starting point is the intersection point 2G. It becomes a relationship that becomes a fold line (fold line Y2 (1)) connecting 1G,
Also, if we consider a group of fold lines connecting the intersection points 3E, 3F, 3G, and 3H, a fold line connecting the intersection points 3F and 3E (fold line X1 (3)) is a symmetric line, and the intersection point is the intersection point 3F. A straight line reflecting a fold line (fold line Y1 (2)) connecting 3F and 2F and a fold line (fold line X2 (3)) connecting the intersection points 3F and 3G with a symmetric line, and starting from the intersection point 3F, the intersection point 3F The bisector of the fold line (fold line Y1 (2)) connecting 2F and 2F becomes the fold line (fold line Y1 (3)) connecting the intersections 3F and 4F and connecting the intersections 3G and 3F A fold line connecting the intersection points 3G and 3H with a fold line (fold line Y2 (2)) connecting the intersection points 3G and 2G with the fold line (fold line X2 (3)) as the symmetric line and the intersection point 3G as the starting point The line (fold line X2 (3)) is a symmetric line, and the intersection 3F is the starting point. The bisector of the fold line connecting the points 3G and 2G (fold line Y2 (2)) becomes the fold line (fold line Y1 (3)) connecting the intersection points 3G and 4G. Just keep
Folding structure that can fold a sheet surrounded by intersections 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, 1E The angle formed by the fold line connecting the intersections 2J and 2K and the fold line connecting the intersections 2J and 2H of the group of fold lines that are continuously connected by valley folds or mountain folds in the body, or opposite, but the intersection The angle formed by the fold line connecting 2H and 2J and the fold line connecting intersections 2H and 2G, the angle formed by the fold line connecting intersections 3J and 3K and the fold line connecting intersections 3J and 3H, and vice versa, Different from the angle formed by the fold line connecting the intersections 3H and 3J and the fold line connecting the intersections 3H and 3G, the positive line given at the intersection of the group of fold lines where the fold lines are connected continuously by valley folds or mountain folds By giving a new angle to the negative angle, it is also linear , Also a group of leading fold line while a valley fold on each fold line and mountain fold Metropolitan turnover, by giving a new angle, so that collapsible.
In addition, although the deformation | transformation area | region is made to the 3rd surface element group extended in 1 row, the fold line connected continuously by a valley fold or a mountain fold is made into a symmetrical line, and the both folded lines made into the symmetrical line are connected. Starting from the intersection point, the bisector of the two straight lines that reflects the fold line that connects the valley fold and the mountain fold for each fold line is connected while the valley fold and the mountain fold are switched for each fold line. If there is a fold line relationship, it can be increased.
In other words, the folding structure that can fold all sheets, even outside the deformation area, is an intersection where the fold lines are connected continuously by valley folds or mountain folds, and the fold lines are connected as symmetric lines. Starting from, the bisector of the two straight lines reflecting the fold line that connects the valley fold and the mountain fold for each fold line is extended, and the fold that connects the valley fold and the mountain fold for each fold line is connected. There is a relationship that becomes a line. However, fold lines that are connected continuously by valley folds or mountain folds are symmetric lines, and fold lines that are connected while valley folds and mountain folds are switched for each fold line, starting from the intersection of both fold lines that are symmetric lines. This relationship is only difficult to understand because the two projected straight lines that line up exactly overlap.

Now, a method for creating a deformation area will be described.
As can be seen from FIGS. 4, 5, 6, and 7, the shape of the surface element in the deformation region can be variously created because of the shape of the first surface element. In other words, if any four points constituting the second surface element at an arbitrary stage are determined, it is considered that the subsequent points are inevitably formed. However, there are restrictions on any of the four points that make up the second surface element at any stage, and not everywhere.
More specifically, a sheet surrounded by intersections 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, and 1E. In the boundary part, which is a deformation area of the foldable structure part that can be folded, is folded in a group of fold lines in the boundary part, so the two fold lines that intersect the fold line in the boundary part are not fold lines in the boundary part. When folded, one of them needs to be on one of the fold lines, so the angle between the fold line at the boundary and the fold line that intersects the fold line at the boundary that is not the fold line at the boundary is determined in advance. Therefore, the angle cannot be changed.
The angle formed by the fold line connecting the intersections 2E and 1E and the fold line connecting the intersections 2E and 2F, the angle formed by the fold line connecting the intersections 3E and 2E and the fold line connecting the intersections 3E and 3F, and the intersections 4E and 3E are connected. The angle formed by the fold line connecting the fold line and the intersections 4E and 4F is an angle that cannot be changed.
On the line where the angle is not changed, any one of the intersection 1F, the intersection 2F, the intersection 3F, the intersection 4F, and the intersection 5F is determined at an arbitrary position, and further, at an arbitrary position on the adjacent line. Define another point.
In addition, the sheet surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4K, 3K, 2K, 1K, 1J, 1H, 1G, 1F, and 1E can be folded. This is an angle at which the basic folding angle of the third surface element group, repeated from the connected portion, which is the deformation area of the folding structure portion, cannot be changed.
The basic folding angle is an angle at which the positive and negative slopes are alternately repeated every time the intersection is sandwiched, and the angle formed by the folding line connecting the intersections 1J and 1H and the folding line connecting the intersections 1J and 1K, An angle formed by a fold line connecting 2H and a fold line connecting intersections 2J and 2K, an angle formed by a fold line connecting intersections 3J and 3H and a fold line connecting intersections 3J and 3K, and a fold line connecting intersections 4J and 4H and intersection 4J The angle formed by the fold line connecting 4K and 4K, the angle formed by the fold line connecting intersections 5J and 5H and the fold line connecting intersections 5J and 5K, the fold line connecting intersections 1H and 1G, and the fold line connecting intersections 1H and 1J Angle, the angle formed by the fold line connecting the intersections 2H and 2G and the fold line connecting the intersections 2H and 2J, the angle formed by the fold line connecting the intersections 3H and 3G and the fold line connecting the intersections 3H and 3J, and connecting the intersections 4H and 4G The corner formed by the fold line connecting the fold line and the intersections 4H and 4J Is an angle fold line makes connecting fold line and the intersection 5H and 5J connecting intersection 5H and 5G.
The angle formed by the fold line connecting the intersection points 2H and 1H and the fold line connecting the intersection points 2H and 2G, the angle formed by the fold line connecting the intersection points 3H and 2H, and the fold line connecting the intersection points 3H and 3G, and the intersection points 4H and 3H are connected. This is the angle formed by the fold line connecting the fold line and the intersection points 4H and 4G.
On the line where the angle is not changed, any one of the intersection 1H, the intersection 2H, the intersection 3H, the intersection 4H, and the intersection 5H is set at an arbitrary position, and further, an arbitrary position on the adjacent line Another point is defined.
However, the relationship between any two points on the first surface element group side and any two points on the third surface element group side is, among the two arbitrary points on the first surface element group side, One of the points and any two points on the third surface element group side must be positioned so as to be a fold line.
Specifically, folding that enables folding of the sheet surrounded by the intersection points 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 5J, 5K, 4H, 3H, 2H, 1H, 1G, 1F, 1E In the structure, the intersection point 1F, the intersection point 2F, the intersection point 1G, and the intersection point 2G are arbitrary four points, the intersection point 1F, the intersection point 2F, the intersection point 2G, and the intersection point 3G are arbitrary four points, or the intersection point 2F and the intersection point 3F Intersection 1G and intersection 2G are any four points, intersection 2F, intersection 3F, intersection 2G and intersection 3G are any four points, or intersection 2F, intersection 3F, intersection 3G and intersection 4G are any four points Or the intersection point 3F, the intersection point 4F, the intersection point 2G, and the intersection point 3G are arbitrary four points, the intersection point 3F, the intersection point 4F, the intersection point 3G, and the intersection point 4G are arbitrary four points, or the intersection point 3F and the intersection point 4F Intersection 4G and intersection 5G are any 4 points, or intersection 4F and intersection The following intersections and folding lines can be selected in 10 ways: F, intersection 3G, and intersection 4G are any 4 points, or intersection 4F, intersection 5F, intersection 4G, and intersection 5G are any 4 points. An angle is necessarily formed. In the case where only the fold line is considered, in the first stage, the fold line X1 (1), the fold line X1 (2), the fold line X2 (1), and the fold line X3 (2) are set to arbitrary lengths. Alternatively, the fold line X1 (1), the fold line X1 (2), the fold line X2 (1), and the fold line Y2 (1) are set to arbitrary lengths, or the fold line X1 (1) and the fold line X1 (2 ), Fold line X2 (2), and fold line X3 (1) have arbitrary lengths, or fold line X1 (1), fold line X1 (2), fold line X2 (2), and fold line Y2 (1 ) To an arbitrary length, fold line X1 (1), fold line X1 (2), fold line X3 (1) and fold line X3 (2) to an arbitrary length, or fold line X1 ( 1), the fold line X1 (2), the fold line X3 (1), and the fold line Y2 (1) have arbitrary lengths, or the fold line X1 (1), the fold line X1 (2), and the fold line X3 ( 2) and fold line Y2 (1 Or the folding line X1 (1), the folding line Y1 (1), the folding line X2 (1), and the folding line X3 (2), or the folding line X1 (1 ), Fold line Y1 (1), fold line X2 (1), and fold line Y2 (1) have arbitrary lengths, or fold line X1 (1), fold line Y1 (1), and fold line X2 (2 ) And fold line X3 (1) are set to arbitrary lengths, or fold line X1 (1), fold line Y1 (1), fold line X2 (2), and fold line Y2 (1) are set to arbitrary lengths. Or the fold line X1 (1), the fold line Y1 (1), the fold line X3 (1), and the fold line X3 (2) have arbitrary lengths, or the fold line X1 (1) and the fold line Y1 ( 1), the fold line X3 (1), and the fold line Y2 (1) have arbitrary lengths, or the fold line X1 (1), the fold line Y1 (1), the fold line X3 (2), and the fold line Y2 ( 1) Is it an arbitrary length? The fold line X1 (2), the fold line Y1 (1), the fold line X2 (1), and the fold line X3 (2) are set to arbitrary lengths, or the fold line X1 (2) and the fold line Y1 (1) The folding line X2 (1) and the folding line Y2 (1) are set to arbitrary lengths, or the folding line X1 (2), the folding line Y1 (1), the folding line X2 (2), and the folding line X3 (1) are set. The fold line X1 (2), the fold line Y1 (1), the fold line X2 (2), and the fold line Y2 (1) may be any length, or the fold line X1 (2). The fold line Y1 (1), the fold line X3 (1), and the fold line X3 (2) are set to arbitrary lengths, or the fold line X1 (2), the fold line Y1 (1), and the fold line X3 (1) The fold line Y2 (1) is set to an arbitrary length, or the fold line X1 (2), the fold line Y1 (1), the fold line X3 (2), and the fold line Y2 (1) are set to an arbitrary length. There are 21 streets, with one step Since 1 kinds, four times, the selection of 84 types, the intersection between the folding line and the angle of the latter, is inevitably formed. Of course, it is possible to determine not only the intersection point and the folding line but also the combination of the intersection point and the folding line, the folding line and the angle, the intersection point and the folding line and the angle, and the like.

The inevitable formation process will be further described assuming that the intersection 2F, the intersection 3F, the intersection 1G, and the intersection 2G are determined.
To form the intersection point 1F, a fold line (fold line Y1 (2)) connecting the intersection points 2F and 3F and a fold line (fold line X1 (2)) connecting the intersection points 2F and 2E are created as symmetry lines. Is a line of intersection 2F (indicated by a two-dot broken line in FIG. 4), a fold line connecting the intersections 2F and 3F (fold line Y1 (2)), and a fold line connecting the intersections 2F and 2G (fold line X2 (2)) ) Created as a symmetric line, the origin is the line of intersection 2F (indicated by a two-dot broken line in FIG. 4), the origin is the bisector of intersection 2F, and the fold line connecting intersections 1D and 1E Is intersected with a line extending from 1E to form an intersection 1F and reach the edge to complete the formation.
Similarly, in order to form the intersection point 3G, a fold line connecting the intersection points 2G and 1G (fold line Y2 (1)) and a fold line connecting the intersection points 2G and 2H (fold line X3 (2)) are created as symmetry lines. The starting point is the line of intersection 2G (indicated by a two-dot broken line in FIG. 4), the fold line connecting the intersections 2G and 1G (fold line Y2 (1)), and the fold line connecting the intersections 2G and 2F (fold line X2). (2)) as a symmetric line, a bisector of which the starting point is the intersection 2G (indicated by a two-dot broken line in FIG. 4), and a fold line connecting the intersections 3H and 3J. The intersection 3G is formed by the intersection of the lines extending from 2G that face each other.
Furthermore, in order to form the intersection point 4F, a fold line (fold line Y1 (2)) connecting the intersection points 3F and 2F was created with a fold line connecting the intersection points 3F and 3E (fold line X1 (3)) as a symmetrical line. , A line starting from the intersection 3F (indicated by a two-dot broken line in FIG. 4), a fold line connecting the intersections 3F and 2F (fold line Y1 (2)), and a fold line connecting the intersections 3F and 3G (fold line X2 ( 3)) created as a symmetric line, the starting point is the line of intersection 3F (indicated by a two-dot broken line in FIG. 4), the starting point is the bisector of intersection 3F, and the fold line connecting intersections 4D and 4E The intersection point 4F is formed by the intersection of the starting point and the line extending from 4E,
In order to form the intersection point 4G, a fold line (fold line Y2 (2)) connecting the intersection points 3G and 2G is created as a symmetric line with a fold line connecting the intersection points 3G and 3F (fold line X2 (3)). Is a line of intersection 3G (indicated by a two-dot broken line in FIG. 4), a fold line connecting the intersections 3G and 2G (fold line Y2 (2)), and a fold line connecting the intersections 3G and 3H (fold line X3 (3) ) Created as a symmetric line, the origin is the line of intersection 3G (indicated by a two-dot broken line in FIG. 4), the origin is the bisector of intersection 3G, and the fold line connecting intersections 4J and 4H Intersects with a line extending from 4H to form an intersection point 4G,
In order to form the intersection 5F, a fold line (fold line Y1 (3)) connecting the intersections 4F and 3F is created, and a fold line (fold line X1 (4)) connecting the intersections 4F and 4E is created as a symmetric line. Is a line of intersection 4F (indicated by a two-dot broken line in FIG. 4), a fold line connecting the intersections 4F and 3F (fold line Y1 (3)), and a fold line connecting the intersections 4F and 4G (fold line X2 (4)) ) Created as a symmetric line, the origin is the line of intersection 4F (indicated by a two-dot broken line in FIG. 4), the origin is the bisector of intersection 4F, and the fold line connecting intersections 5D and 5E Intersects with a line extending from 5E to form an intersection 5F and reach the edge to complete the formation,
In order to form the intersection 5G, a fold line (fold line Y2 (3)) connecting the intersections 4G and 3G and a fold line (fold line X2 (4)) connecting the intersections 4G and 4F are created as symmetry lines. Is a line of intersection 4G (indicated by a two-dot broken line in FIG. 4), a fold line connecting the intersections 4G and 3G (fold line Y2 (3)), and a fold line connecting the intersections 4G and 4H (fold line X3 (4)) ) As a symmetric line, the origin is the line of intersection 4G (indicated by a two-dot broken line in FIG. 4), the origin is the bisector of intersection 4G, and the fold line connecting intersections 5J and 5H Intersects with a line extending from 5H to form an intersection 5G and reach the edge to complete the formation.

If the formation cannot be inevitably performed, it is necessary to redo the initial determination because the initial determination has selected an extreme place or an extreme angle. Then, I will explain in detail what is inevitably impossible to form.
The four intersections to be determined first are folding that enables folding of the sheet surrounded by the intersections 1E, 2E, 3E, 4E, 5E, 5F, 5G, 5H, 4H, 3H, 2H, 1H, 1G, 1F, and 1E. Suppose that four intersection points are not selected outside the structure.
In addition, the bisector that is inevitably formed in the first surface element group is a group of fold lines connecting the intersection points 1E, 2E, 3E, 4E, and 5E before intersecting with the fold line that does not change the angle. Do not cross.
Similarly, the bisector inevitably formed in the third surface element group is a group of fold lines connecting the intersection points 1H, 2H, 3H, 4H, and 5H before crossing the fold line that does not change the angle. Is not to exceed.
Further, the bisector inevitably formed in the first surface element group bisects inevitably formed in the third surface element group before intersecting with the folding line that does not change the angle. Do not cross the line. Conversely, the bisector inevitably formed in the third surface element group is inevitably formed in the first surface element group before intersecting with the folding line that does not change the angle. Do not cross the line.

In addition, in the folding structure that can fold two sheets, one of the two regions divided by each of the one or more boundary fold lines has alternately positive and negative angles, and mountain folds and valley folds. A group of fold lines in which either one of the continuous fold lines intersects the boundary fold line without changing with the other, and the other is a group of fold lines in which mountain folds and valley folds alternate at each intersection point. Even if the boundary part is not a polygonal line but a flexible material, a material having elasticity, and a material that has both flexibility and elasticity, the boundary part is expanded or folded. If you repeat, you will get a similar polyline.

  FIG. 8 shows a folding structure that can fold a sheet according to an embodiment of the present invention, and one of the two regions divided by each of the boundary fold lines alternately has positive and negative angles. A group of fold lines in which one of mountain folds and valley folds does not alternate with the other is a region where the boundary fold line intersects, and the other is a mountain fold and a valley fold alternate at each intersection. In the region where the fold line group intersects the boundary fold line, the center line of the fold line group that alternates between the positive and negative angles intersecting the boundary fold line and the boundary fold line are no longer perpendicular, In addition, a perspective explanatory view of a folding structure that can fold a group of fold lines in which mountain folds and valley folds alternate at each intersection that intersects the boundary fold line, and a sheet in which the boundary fold line is no longer perpendicular. It is. 9 is a developed plan view of FIG.

The folding structure that can fold the sheet according to this embodiment is surrounded by intersections 1a, 2a, 3a, 4a, 5a, 5b, 5c, 5d, 5e, 4e, 3e, 2e, 1e, 1c, 1b, 1a. A folding structure that can fold the sheet, and a sheet surrounded by intersections 1e, 2e, 3e, 4e, 5e, 5f, 5g, 5h, 5j, 4j, 3j, 2j, 1j, 1h, 1g, 1e Folding structures that can be folded are connected by a group of continuous straight folding lines connecting the intersections 1e, 2e, 3e, 4e, and 5e.

There are only two ways of folding the folding structure that allows the sheet to be folded, and the folding method in this explanatory diagram is performed by intersecting points 1b, 2b, 3b, which are alternately at positive and negative angles. A group of continuous fold lines connecting 4b and 5b, a group of continuous fold lines connecting intersections 1e, 2d, 3d, 4d and 5d, and a continuous fold line connecting intersections 2e, 2f, 2g, 2h and 2j. A group of continuous folding lines connecting the group and the intersections 4e, 4f, 4g, 4h, 4j is a continuous mountain fold,
At each intersection, a group of continuous fold lines connecting the intersections 1c, 2c, 3c, 4c, and 5c, and alternating folds connecting the intersections 3e, 3f, 3g, 3h, and 3j, with positive and negative angles alternately. A group of lines and a group of continuous folding lines connecting the straight intersections 1e, 2e, 3e, 4e, and 5e form a continuous valley fold.
Non-continuous mountain folds include a fold line connecting intersections 2a and 2b, a fold line connecting intersections 2c and 2d, a fold line connecting intersections 3b and 3c, a fold line connecting intersections 3d and 3e, and intersections 4a and 4b. , A fold line connecting intersections 4c and 4d, a fold line connecting intersections 2f and 3f, a fold line connecting intersections 4f and 5f, a fold line connecting intersections 1g and 2g, and intersections 3g and 4g , A fold line connecting intersections 2h and 3h, and a fold line connecting intersections 4h and 5h,
The discontinuous valley folds are a fold line connecting the intersection points 2b and 2c, a fold line connecting the intersection points 2d and 2e, a fold line connecting the intersection points 3a and 3b, a fold line connecting the intersection points 3c and 3d, and the intersection points 4b and 4c. , A fold line connecting intersections 4d and 4e, a fold line connecting intersections 1f and 2f, a fold line connecting intersections 3f and 4f, a fold line connecting intersections 2g and 3g, and intersections 4g and 5g , A fold line connecting the intersection points 1h and 2h, and a fold line connecting the intersection points 3h and 4h.

Of the two regions divided by each of the boundary fold lines of the folding structure that can fold the sheet, the folding structure that can fold the sheet, one of them alternately forms positive and negative angles, A group of fold lines where one of mountain folds and valley folds does not alternate with the other is a region where the boundary fold lines intersect, and the other is a fold where mountain folds and valley folds alternate at each intersection. A group of lines intersects the boundary fold line, intersects the boundary fold line, intersects the boundary fold line, and intersects the boundary fold line with the center line of the fold line group and the boundary fold line alternately alternating between the positive and negative angles. The fold line group where the mountain fold and the valley fold alternate at each intersection and the boundary fold line are connected at an angle other than a right angle because there is no need to have a deformable structure for connection. The structure is relatively easy. It should be noted that there is a group of two fold lines that intersect with a group of connected fold lines that are folded when they are folded at the connecting portion, on the line of one fold line group. There is another group of fold lines.
Specifically, the midpoint of the fold line connecting the intersections 1e and 2e, the line connecting the midpoints of the fold line connecting the intersections 2e and 3e, the midpoint of the fold line connecting the intersections 1e and 2d, and the intersection 2d The angle connecting the middle point of the fold line connecting 3d and 3d is the intersection point 1e as the starting point,
A fold line connecting the intersections 1e and 2e, a line connecting the midpoints of the fold lines connecting the intersections 2e and 3e, a midpoint of the fold line connecting the intersections 1e and 2f, and a fold line connecting the intersections 2f and 3f If the line connecting the midpoints is not smaller than the angle having the starting point as the intersection 1e, interference occurs.
Since the group of continuous valley fold lines connecting the intersections 1e, 2e, 3e, 4e, and 5e is linear, the fold line connecting the intersections 2e and 2d overlaps with the fold line connecting the intersections 2e and 2f. The fold line connecting 3e and 3d overlaps the fold line connecting the intersections 3e and 3f, the fold line connecting the intersections 4e and 4d is overlapped with the fold line connecting the intersections 4e and 4f, and the fold line connecting the intersections 5e and 5d is , Overlaps the fold line connecting the intersections 5e and 5f.

  FIG. 10 shows a folding structure that can fold a sheet according to an embodiment of the present invention, and one of the two regions divided by each of the boundary fold lines has an angle of positive and negative alternately. A group of fold lines in which one of mountain folds and valley folds does not alternate with the other is a region where the boundary fold line intersects, and the other is a mountain fold and a valley fold alternate at each intersection. FIG. 5 is a perspective explanatory view of a folding structure in which a sheet in which a group of fold lines intersects with a boundary fold line and an angle is distributed by assigning angles to the area itself can be folded. FIG. 11 is a developed plan view of FIG.

The folding structure that can fold the sheet according to this embodiment is surrounded by intersections A1, A2, A3, A4, A5, B5, C5, D5, E5, E4, E3, E2, E1, C1, B1, A1. Folded structure that can fold the sheet, and surrounded by intersections E1, E2, E3, E4, E5, F5, G5, H5, J5, J4, J3, J2, J1, H1, G1, F1, E1 The folding structures that can fold the sheets are connected by continuous straight folding lines connecting the intersections E1, E2, E3, E4, and E5.

There are only two ways to fold this foldable structure, and the way of folding in this explanatory diagram is a continuous connection between the intersections B1, B2, B3, B4, and B5, in which positive and negative angles are alternated at each intersection. A group of folding lines, a group of continuous folding lines connecting the intersections E1, D2, D3, D4, D5, a group of continuous folding lines connecting the intersections E2, F2, G2, H2, J2, and an intersection E4, A group of continuous fold lines connecting F4, G4, H4, and J4 is a continuous mountain fold,
At each intersection, a group of continuous folding lines connecting the intersections C1, C2, C3, C4, and C5 and alternately folding positive and negative angles, and continuous folding connecting the intersections E3, F3, G3, H3, and J3 A group of continuous folding lines connecting the line group and the linear intersections E1, E2, E3, E4, and E5 form a continuous valley fold.
Non-continuous mountain folds include a fold line connecting intersections A2 and B2, a fold line connecting intersections C2 and D2, a fold line connecting intersections B3 and C3, a fold line connecting intersections D3 and E3, and intersections A4 and B4. A fold line connecting the intersection points C4 and D4, a fold line connecting the intersection points F2 and F3, a fold line connecting the intersection points F4 and E5, a fold line connecting the intersection points G1 and G2, and the intersection points G3 and G4. A fold line connecting the intersections H2 and H3, and a fold line connecting the intersections H4 and H5,
The discontinuous valley folds are a fold line connecting the intersection points B2 and C2, a fold line connecting the intersection points D2 and E2, a fold line connecting the intersection points A3 and B3, a fold line connecting the intersection points C3 and D3, and the intersection points B4 and C4. , A fold line connecting intersections D4 and E4, a fold line connecting intersections F1 and F2, a fold line connecting intersections F3 and F4, a fold line connecting intersections G2 and G3, and intersections G4 and G5 , A fold line connecting the intersections H1 and H2, and a fold line connecting the intersections H3 and H4.

Of the two regions divided by each of the boundary fold lines of the folding structure that can fold the sheet, the folding structure that can fold the sheet, one of them alternately forms positive and negative angles, A group of fold lines where one of mountain folds and valley folds does not alternate with the other is a region where the boundary fold lines intersect, and the other is a fold where mountain folds and valley folds alternate at each intersection. A group of lines intersects the boundary fold line, intersects the boundary fold line, intersects the boundary fold line, and intersects the boundary fold line with the center line of the fold line group and the boundary fold line alternately alternating between the positive and negative angles. The group of fold lines where the mountain fold and valley fold alternate at each intersection and the boundary fold line are connected at an angle other than a right angle because the angle is distributed to the entire folding structure that allows the sheet to be folded. Has realized. In order to distribute the angle, the angle is distributed in each region of the folding structure itself that can fold the sheet.
That is, the folding structure that can fold the sheet surrounded by the intersections A1, A2, A3, A4, A5, B5, C5, D5, E5, E4, E3, E2, E1, C1, B1, A1, The angle is assigned to a group of fold lines that change the way of folding.
In addition, a folding structure that can fold a sheet surrounded by intersections E1, E2, E3, E4, E5, F5, G5, H5, J5, J4, J3, J2, J1, H1, G1, F1, E1. At each intersection, the angles are assigned to a group of continuous fold lines in which positive and negative angles are alternated and the folding method is the same.

Specifically, the folding is such that the sheet surrounded by the intersections E1, E2, E3, E4, E5, F5, G5, H5, J5, J4, J3, J2, J1, H1, G1, F1, E1 can be folded. In the structure, a linear group of fold lines connecting the intersections H5, H4, H3, H2, and H1, a linear group of fold lines connecting the intersections G5, G4, G3, G2, and G1, and a linear shape The group of fold lines connecting the intersections F5, F4, F3, F2, and F1 and the group of fold lines connecting the straight intersections E5, E4, E3, E2, and E1 are not all parallel, and the young number side is It is getting wider.
In the folding structure in which the sheet surrounded by the intersections A1, A2, A3, A4, A5, B5, C5, D5, E5, E4, E3, E2, E1, C1, B1, A1 can be folded,
A fold line connecting the intersection points E1 and D2, a fold line connecting the intersection points C1 and C2, and an intersection point of the plane element group surrounded by the intersection points E2, E1, C1, B1, A1, A2, B2, C2, D2, E2, and E1 The fold line connecting B1 and B2, the fold line connecting the intersections A1 and A2, all are not parallel, have an angle, determine the length, and then inevitably form a fold line,
A fold line connecting the intersection points E2 and D3, a fold line connecting the intersection points C2 and C3, and an intersection point of the plane element group surrounded by the intersection points E3, E2, C2, B2, A2, A3, B3, C3, D3, E3, and E2. The fold line connecting B2 and B3, the fold line connecting the intersections A2 and A3, all are not parallel, have an angle, determine the length, and then inevitably form a fold line,
A fold line connecting the intersection points E3 and D4, a fold line connecting the intersection points C3 and C4, and an intersection point of the plane element group surrounded by the intersection points E4, E3, C3, B3, A3, A4, B4, C4, D4, E4, and E4 A fold line connecting B3 and B4, a fold line connecting intersections A3 and A4, all are not parallel, have an angle, determine the length, and then inevitably form a fold line,
A fold line connecting the intersection points E4 and D5, a fold line connecting the intersection points C4 and C5, and an intersection point of the surface element group surrounded by the intersection points E5, E4, C4, B4, A4, A5, B5, C5, D5, E5, and E5 The fold line connecting B4 and B5, the fold line connecting the intersections A4 and A5, all are not parallel, have an angle, determine the length, then inevitably form a fold line and gradually tilt Giving.

FIG. 12 is a perspective explanatory view of a foldable structure having a regular hexahedron shape made of a foldable structure that can fold a sheet according to an embodiment of the present invention and that can fold the sheet. FIG. 13 is a developed plan view of FIG.
In these two figures, not all intersection points are shown. In the developed plan view of FIG. 13, a group of continuous horizontal fold lines and a group of vertical fold lines are used, and a group of horizontal fold lines is capitalized. Alphabet symbols are assigned, and in the group of vertical folding lines, lowercase alphabet symbols are assigned, and the intersections are described by arranging the assigned symbols in overlapping positions.

The folding structure that can fold the sheet according to this embodiment includes intersections Aj, Bj, Cj, Dj, Ej, Fj, Fk, Fm, Fn, Fp, Ep, Dp, Cp, Bp, Ap, An, Am , A folded structure of a double corrugated expandable structure surrounded by Ak, Aj,
Intersection point Fa, Ga, Ha, Ja, Ka, Ma, Mb, Mc, Md, Me, Mf, Mg, Mh, Mj, Mk, Mm, Mn, Mp, Mq, Mr, Ms, Mt, Kt, Jt, Ht , Gt, Ft, Fs, Fr, Fq, Fp, Fn, Fm, Fk, Fj, Fh, Fg, Ff, Fe, Fd, Fc, Fb, Fa ,
Folding structure that can fold a sheet surrounded by intersections Mj, Nj, Pj, Qj, Rj, Sj, Sk, Sm, Sn, Sp, Rp, Qp, Pp, Np, Mp, Mn, Mm, Mk, Mj Consist of body,
A group of fold lines connecting the intersection points Fj, Fk, Fm, Fn, and Fp and a group of fold lines connecting the intersection points Mj, Mk, Mm, Mn, and Mp are connected.

There are only two ways of folding the folding structure that allows the sheet to be folded, and the folding method in this explanatory diagram is based on the intersections Bj, Bk, Bm, A group of fold lines connecting Bn and Bp, a group of fold lines connecting intersections Dj, Dk, Dm, Dn and Dp, a group of fold lines connecting intersections Fc, Gc, Hc, Jc, Kc and Mc, and intersections A group of folding lines connecting Fg, Gg, Hg, Jg, Kg, Mg, a group of folding lines connecting the intersections Fm, Gm, Hm, Jm, Km, Mm, and the intersections Fr, Gr, Hr, Jr, Kr, A group of fold lines connecting Mr, a group of fold lines connecting intersections Pj, Pk, Pm, Pn, Pp, and a group of fold lines connecting intersections Rj, Rk, Rm, Rn, Rp;
A linear group of fold lines connecting the intersection points Fj, Fk, Fm, Fn, Fp, a group of fold lines connecting the intersection points Mj, Mk, Mm, Mn, Mp, and the intersection points Fe, Ge, He, Je, Ke , Me, a group of fold lines connecting the intersection points Fj, Gj, Hj, Jj, Kj, Mj, and a valley fold where the intersection points Fp, Gp, Hp, Jp, Kp, Mp are continuous. And
A group of fold lines connecting the intersection points Cj, Ck, Cm, Cn, Cp, and a group of fold lines connecting the intersection points Ej, Ek, Em, En, Ep, alternately forming positive and negative angles at each intersection , A group of fold lines connecting the intersection points Fb, Gb, Hb, Jb, Kb, Mb, a group of fold lines connecting the intersection points Fd, Gd, Hd, Jd, Kd, Md, and the intersection points Ff, Gf, Hf, Jf, A group of fold lines connecting Kf, Mf, a group of fold lines connecting intersections Fh, Gh, Hh, Jh, Kh, Mh, and a group of fold lines connecting intersections Fk, Gk, Hk, Jk, Kk, Mk , A group of fold lines connecting the intersection points Fn, Gn, Hn, Jn, Kn, Mn, a group of fold lines connecting the intersection points Fq, Gq, Hq, Jq, Kq, Mq, and the intersection points Fs, Gs, Hs, Js, A group of fold lines connecting Ks and Ms, a group of fold lines connecting intersections Nj, Nk, Nm, Nn, and Np, and an intersection Qj Qk, Qm, Qn, the mountain-folded group of folding lines are continuous connecting Qp.
The discontinuous valley folds are a fold line connecting intersections Ak and Bk, a fold line connecting intersections An and Bn, a fold line connecting intersections Bm and Cm, a fold line connecting intersections Ck and Dk, and intersections Cn and Dn. A fold line connecting the intersection points Dm and Em, a fold line connecting the intersection points Ek and Fk, a fold line connecting the intersection points En and Fn,
A fold line connecting intersections Ha and Hb, a fold line connecting intersections Ka and Kb, a fold line connecting intersections Gb and Gc, a fold line connecting intersections Jb and Jc, and a fold line connecting intersections Hc and Hd; A fold line connecting intersections Kc and Kd, a fold line connecting intersections Gd and Ge, a fold line connecting intersections Jd and Je, a fold line connecting intersections He and Hf, and a fold line connecting intersections Ke and Kf; A fold line connecting intersections Gf and Gg, a fold line connecting intersections Jf and Jg, a fold line connecting intersections Hg and Hh, a fold line connecting intersections Kg and Kh, and a fold line connecting intersections Gh and Gj; A fold line connecting intersections Jh and Jj, a fold line connecting intersections Hj and Hk, a fold line connecting intersections Kj and Kk, a fold line connecting intersections Gk and Gm, and a fold line connecting intersections Jk and Jm; A fold line connecting the intersections Hm and Hn, a fold line connecting the intersections Km and Kn, and an intersection G , A fold line connecting the intersections Jn and Jp, a fold line connecting the intersections Hp and Hq, a fold line connecting the intersections Kp and Kq, a fold line connecting the intersections Gq and Gr, and an intersection Jq A fold line connecting Jr and Jt, a fold line connecting intersections Hr and Hs, a fold line connecting intersections Kr and Ks, a fold line connecting intersections Gs and Gt, a fold line connecting intersections Js and Jt,
A fold line connecting intersections Mk and Nk, a fold line connecting intersections Mn and Nn, a fold line connecting intersections Nm and Pm, a fold line connecting intersections Pk and Qk, and a fold line connecting intersections Pn and Qn; A fold line connecting intersections Qm and Rm, a fold line connecting intersections Rk and Sk, and a fold line connecting intersections Rn and Sn,
Non-continuous mountain folds include a fold line connecting intersections Am and Bm, a fold line connecting intersections Bk and Ck, a fold line connecting intersections Bn and Cn, a fold line connecting intersections Cm and Dm, and intersections Dk and Ek. A fold line connecting the intersection points Dn and En, a fold line connecting the intersection points Em and Fm,
A fold line connecting intersections Ga and Gb, a fold line connecting intersections Ja and Jb, a fold line connecting intersections Hb and Hc, a fold line connecting intersections Kb and Kc, and a fold line connecting intersections Gc and Gd; A fold line connecting the intersection points Jc and Jd, a fold line connecting the intersection points Hd and He, a fold line connecting the intersection points Kd and Ke, a fold line connecting the intersection points Ge and Gf, and a fold line connecting the intersection points Je and Jf; A fold line connecting intersections Hf and Hg, a fold line connecting intersections Kf and Kg, a fold line connecting intersections Gg and Gh, a fold line connecting intersections Jg and Jh, and a fold line connecting intersections Hh and Hj; A fold line connecting intersections Kh and Kj, a fold line connecting intersections Gj and Gk, a fold line connecting intersections Jj and Jk, a fold line connecting intersections Hk and Hm, and a fold line connecting intersections Kk and Km; A fold line connecting the intersections Gm and Gn, a fold line connecting the intersections Jm and Jn, and an intersection H , A fold line connecting intersections Kn and Kp, a fold line connecting intersections Gp and Gq, a fold line connecting intersections Jp and Jq, a fold line connecting intersections Hq and Hr, and an intersection Kq A fold line connecting the intersections Gr and Gs, a fold line connecting the intersections Jr and Js, a fold line connecting the intersections Hs and Ht, a fold line connecting the intersections Ks and Kt,
A fold line connecting intersections Mm and Nm, a fold line connecting intersections Nk and Pk, a fold line connecting intersections Nn and Pn, a fold line connecting intersections Pm and Qm, and a fold line connecting intersections Qk and Rk; A fold line connecting the intersection points Qn and Rn and a fold line connecting the intersection points Rm and Sm.

Each face of the regular hexahedron is a square surrounded by intersection points Aj, Bj, Cj, Dj, Ej, Fj, Fk, Fm, Fn, Fp, Ep, Dp, Cp, Bp, Ap, An, Am, Ak, Aj. And a square surrounded by intersections Fa, Ga, Ha, Ja, Ka, Ma, Mb, Mc, Md, Me, Ke, Je, He, Ge, Fe, Fd, Fc, Fb, Fa, and an intersection Fe, Ge, He, Je, Ke, Me, Mf, Mg, Mh, Mj, Kj, Jj, Hj, Gj, Fj, Fh, Fg, Ff, Fe and a square surrounded by an intersection Fj, Gj, Hj, Jj , Kj, Mj, Mk, Mm, Mn, Mp, Kp, Jp, Hp, Gp, Fp, Fn, Fm, Fk, Fj and the intersection Fp, Gp, Hp, Jp, Kp, Mp, Mq, Mr, Ms, Mt, Kt, Jt, Ht, Gt, Ft, Fs, Fr A square surrounded by Fq and Fp and an intersection Mj, Nj, Pj, Qj, Rj, Sj, Sk, Sm, Sn, Sp, Rp, Qp, Pp, Np, Mp, Mn, Mm, Mk, Mj Square.
Each connecting fold line of the regular hexahedron includes a group of fold lines connecting the intersection points Fj, Fk, Fm, Fn, and Fp, and a group of fold lines connecting the intersection points Fe, Ge, He, Je, Ke, and Me. A group of folding lines connecting Fj, Gj, Hj, Jj, Kj, Mj, a group of folding lines connecting the intersections Fp, Gp, Hp, Jp, Kp, Mp, and intersections Mj, Mk, Mm, Mn, Mp All the groups of fold lines to be connected are straight valley folds. Note that the group of fold lines connecting the intersection points Fj, Fk, Fm, Fn, and Fp and the group of fold lines connecting the intersection points Mj, Mk, Mm, Mn, and Mp are the boundary fold lines that connect the folding structures having different directions. A group of fold lines connecting the intersection points Fe, Ge, He, Je, Ke, Me, a group of fold lines connecting the intersection points Fj, Gj, Hj, Jj, Kj, Mj, and the intersection points Fp, Gp, Hp. , Jp, Kp, and Mp are a group of fold lines in which the folding structure of the fold structure continues.
In addition, the group of connection folding lines constituting this regular hexahedron is all linear, and there is a group of folding lines in which either one of the mountain folds or the valley folds is continuous with the other, but when assembled, the regular hexahedrons Although the shape is blurred, it can also be a group of continuous folding lines that alternate between positive and negative angles. In this case, it is easy to fold, and in the case of mountain fold, it is difficult to fold in the valley, and in the case of mountain fold, it becomes difficult to fold into the valley and the folding direction is stabilized.
In order to make all fold lines into valley folds in this regular hexahedron unfolded structure, the number of folds must be considered. Specifically, for a square surrounded by intersection points Fj, Gj, Hj, Jj, Kj, Mj, Mk, Mm, Mn, Mp, Kp, Jp, Hp, Gp, Fp, Fn, Fm, Fk, Fj, Considering, the number of folds of a group of fold lines connecting intersections Fj, Gj, Hj, Jj, Kj, Mj is four, and the number of folds of a group of fold lines connecting intersections Fj, Fk, Fm, Fn, Fp is three. One. That is, the number of folds in the group of fold lines connecting the intersections Fj, Gj, Hj, Jj, Kj, Mj must be an even number, and the number of folds in the group of fold lines connecting the intersections Fj, Fk, Fm, Fn, Fp must be odd. I must.
Since the folding structures that can fold sheets in different directions are connected, the deformation areas are the intersection points Fj, Gj, Hj, Jj, Jk, Jm, Jn, Jp, Hp, Gp, Fp, Fn, Fm, Fk. , Fj and a plane element group surrounded by intersections Hj, Kj, Mj, Mk, Mm, Mn, Mp, Kp, Jp, Hp, Hn, Hm, Hk, Hj.
In other words, all the squares surrounded by the intersection points Fj, Gj, Hj, Jj, Kj, Mj, Mk, Mm, Mn, Mp, Kp, Jp, Hp, Gp, Fp, Fn, Fm, Fk, Fj are all in the deformation region. Because
The fold line connecting the intersections Gh and Gj, the fold line connecting the intersections Hh and Hj, the fold line connecting the intersections Jh and Jj, and the fold line connecting the intersections Kh and Kj are all parallel to the fold line connecting the intersections Fh and Fj. Must not
Similarly, all of the fold line connecting the intersection points Gp and Gq, the fold line connecting the intersection points Hp and Hq, the fold line connecting the intersection points Jp and Jq, and the fold line connecting the intersection points Kp and Kq are fold lines connecting the intersection points Fp and Fq. Is not parallel to. The deformation area to eliminate it,
A region surrounded by intersections Ff, Gf, Hf, Jf, Kf, Mf, Mg, Mh, Mj, Kj, Jj, Hj, Gj, Fj, Fh, Fg, Ff;
This is a region surrounded by the intersection points Fp, Gp, Hp, Jp, Kp, Mp, Mq, Mr, Ms, Ks, Js, Hs, Gs, Fs, Fr, Fq, and Fp.

FIG. 14 is a perspective explanatory view of a foldable structure having a regular tetrahedron shape made of a foldable structure that can fold a sheet according to an embodiment of the present invention, and that can fold a sheet. 15 is a developed plan view of FIG.
FIG. 16 is an image development plan view of a folding structure that can fold a sheet in five forms in which a group of planes constituting a solid is connected to two or less plane groups constituting another solid. . In FIG. 16, the side group where the surface groups constituting the solid are connected is shown as a solid line, and the positive and negative angles are alternately formed, and either one of the mountain fold and the valley fold is continuous without changing with the other. The folding line to be shown is indicated by a two-dot broken line, the angles of positive and negative are alternately formed, and the line that intersects with the continuous folding line without any one of the mountain fold and the valley fold is omitted. .

The folding structure that can fold the sheet according to this embodiment is merely a single folding structure. That is, a solid is formed by coasting.
The condition that this single folding structure becomes a three-dimensional structure is that the group of planes constituting the solid, not the plane group of the folding structure, is connected to two or less planes constituting the other solid. is there. If this condition is satisfied, a shape other than the tetrahedron can be created with a single folded structure. Please refer to the image development plan view of tetrahedron, hexahedron, and octahedron in FIG. As a disadvantage, when the intersections overlap due to meandering, the surface becomes small and it becomes difficult to fold.
Specifically, the folding structure surrounded by the intersections Pra, Prb, and Prf, the folding structure that can fold the sheet surrounded by the intersections Prf, Prb, and Prc, and the intersections Prc, Pre, and Prf. A group of linear fold lines in which a foldable structure that can fold an enclosed sheet and a foldable structure that can fold a sheet enclosed by intersections Pre, Prc, and Prd are joined by intersections Prb and Prf , A group of linear fold lines connected by the intersection points Prc and Prf, and a group of linear fold lines connected by the intersection points Prc and Pre, which are connected by valley folds. When the establishment of the condition is verified, the folding structure surrounded by the intersections Pra, Prb, and Prf is connected to only one point of the group of linear fold lines connected by the intersections Prb and Prf, and the intersections Prf, Prb are connected. The folding structure that can fold the sheet surrounded by Prc. A group of linear fold lines connected by intersections Prb and Prf. A foldable structure in which only two points in a group of linear fold lines connected at the intersections Prc and Prf are connected and a sheet surrounded by the intersections Prc, Pre, and Prf can be folded is connected at the intersections Prc and Prf. Only two points of the group of linear fold lines and the group of linear fold lines connected by the intersection points Prc and Pre are connected, and the sheet surrounded by the intersection points Pre, Prc, and Prd can be folded. The folding structure is connected to only one part of a group of linear folding lines connected by the intersections Prc and Pre.

The intersection Prb, intersection Prf, intersection Prc, and intersection Pre are used as starting points, and by overlapping, the angles are evenly distributed to form an equilateral triangle. By making the number of distributions within an equilateral triangle an even number, the method of folding connection fold lines is unified.

  FIG. 17 is a perspective explanatory view showing a state in which a folding structure that can fold a seat, which is a cover body for a motorcycle according to an embodiment of the present invention, is completely attached to the motorcycle.

In the protective cover according to this embodiment, the front side surface 01, the left side surface 02, and the rear side surface 03 are configured by the same folding structure, and the left side surface 02 is the part of the fold line that connects the front side surface 01 and the left side surface 02. The group of fold lines connecting the rear side surface 03 is a group of continuous fold lines that fold in the same direction, alternately repeating positive and negative slopes at the intersections. In addition, the ceiling surface 4 and the right side surface 5 are the same folding structure, and the group of fold lines connecting the ceiling surface 4 and the right side surface 5 also repeats positive and negative slopes alternately at the intersection. Is a group of fold lines that are continuously connected by valley folds or mountain folds.
By connecting the front side surface 01 and the right side surface 05 of the folding structure that can fold sheets having different folding directions, a hexahedron having no bottom is formed. This configuration can be connected with one slide fastener and a hook-and-loop fastener. In order to construct a hexahedron having no bottom with a folding structure that can fold two sheets having different folding directions, the right side surface 05, the front side surface 01, the left side surface 02, and the rear side surface 03 are combined into one sheet. A foldable structure that can be folded is also possible, and only one ceiling surface 04 can be formed, and a foldable structure that allows sheets to be folded. In addition, the combination of the folding structure which can fold the sheet | seat in which a connection location and a folding direction differ can be considered.

  The surface element part of the folding structure that can fold the sheet is not a flexible fabric, but is made of a hard material that is difficult to bend, such as foamed styrene or plastic, and the folding structure that can fold the sheet. A portion connecting the constituting surface elements is formed of a material such as a hinge, a flexible cloth such as a cloth, or a plastic sheet. In addition, the part that joins the folding structure that can fold sheets that can fold sheets that can fold sheets that have different directions in which the edge part and zigzag mountain folds and valley folds continue is also made of a flexible fabric. Rather, foamed styrene, plastic, or a composite of them, formed of a hard material that is difficult to bend, and the part that connects the figures that make up the folding structure that can fold the sheet is also a flexible cloth like cloth, or It is made of a material such as a plastic sheet. In addition, the heat insulation sheet is affixed on the engine and muffler part which become high temperature.

  Further, in order to maintain a hexahedral structure without a bottom, the three side surfaces except the right side surface 05 and the ceiling surface 04 are fixed with a slide fastener 0A, and the rear side surface 03 and the right side on the extension line of the slide fastener Both surfaces 05 are fixed by slide fasteners 0A. In addition, a hook, a button, a snap, or a hook-and-loop fastener can be used instead of the slide fastener 0A.

  Furthermore, because the motorcycle does not have a large flat surface on the inner side of the protective cover, the intermediate stabilizer 0B that supports the shape in the middle of attachment and detachment is located at the highest position before and after the motorcycle. A slide jig 0E that slides on the intermediate stabilizer 0B is fixed by a string 0F, which is fixed by a front motorcycle dedicated vehicle body mounting jig 0C and a rear motorcycle dedicated vehicle body mounting jig 0D. The intermediate stabilizer 0B can be configured by a stable expanding and contracting rod, but is configured by combining a cheap string and a rubber string, or by a structure including only a rubber string.

  FIG. 18 is a perspective explanatory view of a two-wheeled vehicle cover body according to an embodiment of the present invention, in which a folding structure that can fold a seat is attached to or detached from the motorcycle.

The protective cover according to this embodiment is gathered by the fastening snap 0G with the front side face 01, the left side face 02, and the rear side face 03 folded, and is attached to the intermediate stabilizer 0B by the slide jig 0E and the string 0F. It is in a suspended state. By releasing the retaining snap 0G, it is in the middle of attachment, and when it is slid and pulled to the center, it is also in the middle of attachment / detachment. The slide jig 0E and the string 0F are attached at several places in order to disperse their own weight. Moreover, the slide jig 0E is attached to the near fold line of the fold portion where the protective cover is folded.

FIG. 19 is a motorcycle cover body according to an embodiment of the present invention. The folding structure that can fold the seat is detached from the motorcycle, and the final fastening snap before the storage shape is secured. It is perspective explanatory drawing of the state which is not carried out.

The protective cover according to this embodiment is folded and gathered, except for the last snap. A portion where the front side surface 01 and the left side surface 02 are connected, a portion where the left side surface 02 and the rear side surface 03 are connected, and a portion where the ceiling surface 04 and the right side surface 05 are connected are alternately intersecting positive and negative slopes. A group of continuous fold lines that fold in the same direction. Although there are restrictions such as folding, the size of the folded and gathered shape is the same as the size of the surface elements that make up the folding structure that can fold the sheet. It is determined by the number of times and the thickness. In addition, since the size of the hexahedron has a degree of freedom, a large degree of freedom is given to the design.

FIG. 20 is a perspective explanatory view showing a state in which a folding structure that can fold a seat, which is a motorcycle cover according to an embodiment of the present invention, is completely attached to a bicycle.

This is a state in which the protective cover according to this embodiment is attached to the bicycle. Although it is almost the same as the protective cover of a motorcycle, the bicycle has no handle lock and no rearview mirror, so the intermediate stabilizer 0B is fixed. The side bicycle dedicated car body mounting jig 0I is required. In addition, there are various choices for bicycles, such as the presence or absence of a child seat on the front wheel side, the presence or absence of a front cage, the presence or absence of a child seat on the rear wheel side, or the presence or absence of a rear cage. This can be dealt with only by changing the design of the front bicycle body mounting jig 0H and the rear bicycle body mounting jig 0I.

FIG. 21 is an explanatory perspective view of a state in which a folding structure that can fold a seat, which is an automobile cover body according to an embodiment of the present invention, is completely attached to the automobile.

This is a state in which the protective cover according to this embodiment is mounted on an automobile. Although the roof shape of an automobile has various shapes depending on the vehicle type, there is a flat surface, so an intermediate stable line is not required. However, in order to use the property of the folded structure that expands when the diagonal is pulled, it can be easily attached or detached if there is a hook-attached string or a car body mounting reference jig 0J such as a suction cup. .

  In common with FIGS. 17 to 21, since it has a simple hexahedral shape without a bottom, although there is a size restriction, it does not depend on the individual shape of the bicycle, the motorcycle, the motorcycle, or the automobile. In addition, since a simple hexahedral shape without a bottom can be changed to a polyhedral shape, it can correspond to almost all bicycles, motorcycles, motorcycles, or automobiles.

  It can also be applied to covers that frequently converge, unfold, deploy, and install and remove, storage containers for food that are bulky to store, storage boxes for clothes, outdoor equipment, and the like. Furthermore, it can be applied to a wall that surrounds a simple toilet, a simple shower, and a simple bathroom.

01 Front side 02 Left side 03 Rear side 04 Ceiling
05 Right Side 0A Slide Fastener 0B Intermediate Stabilizer 0C Front Motorcycle Dedicated Car Body Mounting Jig 0D Rear Motorcycle Dedicated Car Body Mounting Jig 0E Slide Jig 0F String 0G Fastening Snap 0H Front Bicycle Dedicated Car Body Mounting Jig 0I Rear Bicycle Dedicated body mounting jig 0J Auto body mounting standard jig

The second of the present invention has a sheet,
The sheet is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
The first fold line group includes a line group that alternates between positive and negative angles at each intersection with the second fold line group, and one or more fold lines that are linear. In each case, one of the mountain fold and the valley fold is continuous without changing with the other , and the mountain fold and the valley fold are changed between the first fold line adjacent to itself. And
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Thereby, the sheet can be expanded three-dimensionally by folding along at least one of the one or more linear first fold lines, and all the surface elements in the sheet are mutually connected. It is a foldable structure in which the sheets can be folded in an overlapping form.

The third of the present invention has a sheet,
The sheet has a plurality of regions divided by one or more boundary fold lines that are one or more fold lines forming a boundary;
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
The first fold line group includes a line group that alternates between positive and negative angles at each intersection with the second fold line group, and includes one or more of the plurality of regions. The region includes one or more fold lines that are linear, each of which is continuous with one of a mountain fold and a valley fold without alternating with the other, and a first fold line adjacent to itself. Mountain folds and valley folds are alternating between
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Of the two regions sandwiching each of the one or more boundary fold lines, one is a first region where the first fold line group intersects the boundary fold line, and the other is the second fold line. A group of lines is a second region intersecting the boundary fold line, and the first fold line group and the second fold line group intersecting the boundary fold line are the boundary fold line. The length of the line segment from the boundary fold line to the nearest intersection is between the first and second fold lines that are continuous with each other without branching. The second fold line is shorter than the first fold line,
When the boundary fold line extends in a straight line without bending at each intersection, the first and second fold lines that are continuous across the boundary fold line have the boundary fold line as the axis of symmetry. Intersect the boundary fold line at an angle that is line symmetric,
When the boundary fold line is bent with alternating positive and negative angles at each intersection, the first and second fold lines continuous across the boundary fold line are the boundary fold lines. Intersecting the boundary fold line at an angle that is a line symmetry axis of the boundary fold line that does not bend each other at the intersection with the line,
In each of the intersections of the first fold line group and the two second fold lines closest to the boundary fold line among the second fold line group in the first region, One and the other of the first fold lines sandwiching the intersection, and one and the other of the second fold lines sandwiching the intersection are the second fold with one of the first fold lines as an axis of symmetry. Line symmetry between a first imaginary line that is symmetric with respect to one of the lines and a second imaginary line that is symmetric with respect to one of the second fold lines with respect to the other of the first fold lines The axis corresponds to the other of the second fold lines,
Thereby folding the sheet along at least one of the one or more boundary fold lines and at least one of the one or more linear first fold lines in the one or more regions. Is a foldable structure that allows the sheet to be folded in such a manner that all the surface elements in the sheet overlap each other.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.
FIG. 1 shows a folding structure that can fold a sheet according to an embodiment of the present invention, and one of the two regions divided by each of the boundary fold lines alternately has positive and negative angles. A group of fold lines in which one of mountain folds and valley folds does not alternate with the other is a region where the boundary fold line intersects, and the other is a mountain fold and a valley fold alternate at each intersection. In the region where the fold line group intersects the boundary fold line, the center line of the fold line group that alternates between the positive and negative angles intersecting the boundary fold line and the boundary fold line become perpendicular, In addition, a perspective explanatory view of a folding structure that can fold a group of fold lines in which mountain folds and valley folds alternate at each intersection that intersects the boundary fold line and a sheet in which the boundary fold line is perpendicular to each other. It is. FIG. 2 is a developed plan view of FIG. 3 is a development plane in which the boundary fold lines in FIG. 2 are alternately formed with positive and negative angles, and either one of the mountain folds or the valley folds is continuous without changing the other. FIG.
By alternating the positive and negative angles, if the angle at any intersection is an obtuse angle, the angle at the next intersection is an acute angle, and if the angle at any intersection is an acute angle, The angle at the next intersection is an obtuse angle. However, this is not the case when there is an inclination or a straight line.
4 is one of the two regions divided by each of the boundary fold lines in FIG. 2, one of which alternately forms positive and negative angles, and either one of mountain fold or valley fold alternates with the other. A group of fold lines that are continuous without crossing the boundary fold line, and the other is a region where a group of fold lines where mountain folds and valley folds alternate at each intersection intersects with the boundary fold line. It is a development plane explanatory view which extracted a boundary fold line circumference fold line. FIG. 5 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created with a different shape. FIG. 6 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape that is not shown in FIGS. FIG. 7 is a developed plan explanatory view in which the excerpt of FIG. 4 according to an embodiment of the present invention is created in a different shape that is not shown in FIGS. 4, 5, or 6. The reference numerals in FIGS. 4, 5, 6, and 7 indicate the number of steps in parentheses. The double broken line is a line projected with a symmetric line, and the angles with black circles are the same angle, and the angles with white circles are the same angle. In addition, a right angle is also shown. In other angle notations, only adjacent angles are the same angle.

Claims (9)

Have a sheet,
The sheet has a plurality of regions divided by one or more boundary fold lines that are one or more fold lines forming a boundary;
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Of the two regions sandwiching each of the one or more boundary fold lines, one is a first region where the first fold line group intersects the boundary fold line, and the other is the second fold line. A group of lines is a second region intersecting the boundary fold line, and the first fold line group and the second fold line group intersecting the boundary fold line are the boundary fold line. The length of the line segment from the boundary fold line to the nearest intersection is between the first and second fold lines that are continuous with each other without branching. The second fold line is shorter than the first fold line,
When the boundary fold line extends in a straight line without bending at each intersection, the first and second fold lines that are continuous across the boundary fold line have the boundary fold line as the axis of symmetry. Intersect the boundary fold line at an angle that is line symmetric,
When the boundary fold line is bent with alternating positive and negative angles at each intersection, the first and second fold lines continuous across the boundary fold line are the boundary fold lines. Intersecting the boundary fold line at an angle that is a line symmetry axis of the boundary fold line that does not bend each other at the intersection with the line,
In each of the intersections of the first fold line group and the two second fold lines closest to the boundary fold line among the second fold line group in the first region, One and the other of the first fold lines sandwiching the intersection, and one and the other of the second fold lines sandwiching the intersection are the second fold with one of the first fold lines as an axis of symmetry. Line symmetry between a first imaginary line that is symmetric with respect to one of the lines and a second imaginary line that is symmetric with respect to one of the second fold lines with respect to the other of the first fold lines The axis corresponds to the other of the second fold lines,
Thereby, by folding along at least one of the one or more boundary fold lines, the sheet can be expanded in three dimensions, and all the surface elements in the sheet overlap each other, A folding structure that can fold the sheet. Have a sheet,
The sheet is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
The group of first fold lines includes one or more linear first fold lines;
Thereby, the sheet can be expanded three-dimensionally by folding along at least one of the one or more linear first fold lines, and all the surface elements in the sheet are mutually connected. A folding structure in which the sheets can be folded in an overlapping form. Have a sheet,
The sheet has a plurality of regions divided by one or more boundary fold lines that are one or more fold lines forming a boundary;
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Of the two regions sandwiching each of the one or more boundary fold lines, one is a first region where the first fold line group intersects the boundary fold line, and the other is the second fold line. A group of lines is a second region intersecting the boundary fold line, and the first fold line group and the second fold line group intersecting the boundary fold line are the boundary fold line. The length of the line segment from the boundary fold line to the nearest intersection is between the first and second fold lines that are continuous with each other without branching. The second fold line is shorter than the first fold line,
When the boundary fold line extends in a straight line without bending at each intersection, the first and second fold lines that are continuous across the boundary fold line have the boundary fold line as the axis of symmetry. Intersect the boundary fold line at an angle that is line symmetric,
When the boundary fold line is bent with alternating positive and negative angles at each intersection, the first and second fold lines continuous across the boundary fold line are the boundary fold lines. Intersecting the boundary fold line at an angle that is a line symmetry axis of the boundary fold line that does not bend each other at the intersection with the line,
In each of the intersections of the first fold line group and the two second fold lines closest to the boundary fold line among the second fold line group in the first region, One and the other of the first fold lines sandwiching the intersection, and one and the other of the second fold lines sandwiching the intersection are the second fold with one of the first fold lines as an axis of symmetry. Line symmetry between a first imaginary line that is symmetric with respect to one of the lines and a second imaginary line that is symmetric with respect to one of the second fold lines with respect to the other of the first fold lines The axis corresponds to the other of the second fold lines,
In one or more of the plurality of regions, the group of first fold lines includes one or more linear first fold lines,
Thereby folding the sheet along at least one of the one or more boundary fold lines and at least one of the one or more linear first fold lines in the one or more regions. A foldable structure in which the sheet can be folded in such a manner that all the surface elements in the sheet overlap each other. Have a sheet,
The sheet has a plurality of regions cut along one or more lines and connected to each other by one or more connecting members in a belt-like and sheet-like manner that can bend and stretch.
Each of the plurality of regions is
A group of first fold lines aligned with each other and a group of second fold lines aligned with each other and intersecting the first fold line group are divided by these fold line groups. Has a group of elements,
Each of the first fold line group alternately forms positive and negative angles at each intersection with the second fold line group, and either the mountain fold or the valley fold alternates with the other. The mountain fold and the valley fold are alternated between the first fold line adjacent to the first fold line.
In each of the second fold line groups, mountain folds and valley folds are alternated at each intersection with the first fold line group, and the same plane elements are adjacent to each other on different sides. Mountain folds and valley folds alternate between the second fold line segments,
Thereby, by folding at least one of the one or more connecting members, the sheet can be expanded in three dimensions, and the sheet can be folded in a form in which all the surface elements in the sheet overlap each other. Folded structure. The folding structure according to any one of claims 1 to 4, wherein, as the three-dimensional development, five faces excluding one face can be formed among six faces of a hexahedron. The folding structure according to claim 5, which is a cover for a motorcycle. The folding structure according to claim 5, which is an automobile cover body. The folding structure according to any one of claims 1 to 4, wherein six faces of a hexahedron can be formed as the three-dimensional development. The folding structure according to any one of claims 1 to 4, wherein four faces of a tetrahedron can be formed as the three-dimensional development.

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