JP2021123357A - Hollow polygonal columnar structure - Google Patents

Abstract

To provide a hollow polygonal columnar structure which is foldable without deforming surfaces by rotating surfaces around each ridge line and polygonal line.SOLUTION: A hollow square columnar structure has a congruent square Vn,1,1 Vn,1,2 Vn,2,2 Vn,2,1 (n=1,2) as bottom and sides V1,i,1 V1,i,2 V2,i,2 V2,i,1 (i=1,2) that fold together with the bottom as "wall sides", and sides V1,1,j V1,2,j V2,2,j V2,1,j (j=1,2) that move with deformation of the bottom without folding themselves as "lid sides". The hollow square columnar structure has a folding configuration at boundary areas between the bottom and the wall sides, a configuration that eliminates surface interference due to folding along the folding lines at the center of the bottom and the wall sides, and a configuration that eliminates surface interference due to folding in the boundary areas between the lid sides and the wall sides.SELECTED DRAWING: Figure 1

Description

The present invention relates to a foldable hollow polygonal columnar structure.

In general, it is widely used to fold a rectangular parallelepiped bag or storage container in whole or in part, and when it is not used as a container such as when storing it, fold it to improve the storability and transport it in that state. Therefore, it is usefully used for improving the efficiency of transportation when there is no content in the container. In the folding method, when folding a closed box, a structure having a developed view as shown in FIG. 22 is formed with ridge lines V _{1, i, j} V _{2, i, j} (i = 1, 2; j = 1, 2). ), V _{2,1, j} V _{2,2, j} (j = 1, 2) joins to form a ridgeline to form a box structure (rectangular parallelepiped). By rotating the surface (wall) around each ridge line and the fold line as a fold line, the fold line is completely folded.

However, this is limited to cases where the surface is made of a material that can be deformed, such as paper or fabric, and if each surface is considered to be a rigid body or if it is not practically easy to bend, it accompanies the rotation of the surface. , Ridge V _{n, i, 1} V _{n, i, 2} (n = 1, 2; i = 1, 2) is overstressed and cannot be folded without breaking the ridge.

This phenomenon is known as the "Bellows Theorem". The theory of bellows is that, for example, as described in Non-Patent Document 1, "generally, a polyhedron cannot change its volume while maintaining the rigidity of the surface". This means that a hexahedron consisting of a rectangular parallelepiped or other quadrangular prism structure cannot be folded at all unless the four ridges parallel to the compression direction are completely cut.

Even if the theory of bellows is avoided by a method other than completely cutting the four ridges parallel to the compression direction of the hexahedron, when a highly rigid surface material having a finite thickness is used, the axis associated with folding is used. The rotation of the surfaces around them interferes with each other due to the thickness of the surfaces and cannot be folded at all or can only be folded incompletely.

R. Connelly, I. Sabitov, and A. Walz. The bellows conjecture. Contributions to Algebra and Geometry, 38 (1): 1-10, 1997.

Constructing a hollow cube, rectangular parallelepiped or polygonal columnar structure with a highly rigid material and folding it has many industrial uses. For example, in the case of a container for transportation, when the luggage is stored and transported in the container, the structural rigidity is maintained, and the empty container can be folded to reduce the volume and transferred to improve the efficiency of transportation. In addition, the structure used as a temporary simple building can be folded and transported, and can be folded even when not in use to improve storage efficiency. However, since a method of folding a rectangular parallelepiped or a polygonal prism structure using a highly rigid material for a surface is not generally known, a technique capable of that is required.

An object of the present invention is to provide a hollow polygonal columnar structure that can be folded without deforming the surface by rotating the surface around each ridge line and each polygonal line.

In order to achieve the above object, according to the present invention, a congruent quadrangle V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2,1} (n = 1, 2) A hollow quadrangular columnar structure that is configured as the bottom surface and can be folded without deformation of the surface by rotating the surface around the hinged line, and the side surfaces V _{1, i, 1} V that can be folded together with the bottom surface. _{1, i, 2} V _{2, i, 2} V _{2, i, 1} (i = 1, 2) is the "wall side surface", and the side surface V _{1, which moves with the deformation of the bottom surface without folding itself When 1, j} V _{1,2, j} V _{2,2, j} V _{2,1, j} (j = 1, 2) is the "side of the lid"
Configuration 1: Folding configuration in the boundary area between the bottom surface and the side surface of the wall.
Configuration 2: A configuration that eliminates surface interference due to folding along the folding line at the center of the bottom surface and the side surface of the wall.
Configuration 3: A hollow square columnar structure having three configurations for eliminating surface interference due to folding in the boundary region between the lid side surface and the wall side surface is provided.
However, in the present specification, the subscript is determined by using (1,1,1) as a reference point and distant from the reference point in any of the three-dimensional directions.

In the configuration 1, the equiangular bisector of the inner angle in the _{bottom surface is drawn from the apex V n, i, j with respect to the apex V n, i, j} constituting the bottom surface, and the end point Q _{n, i, j is drawn in the bottom surface. , 0} is set, and from the end point Q _{n, i, j, 0 , the foot of the perpendicular line segment drawn on the ridge line V n, i, 1} V _{n, i, 2} of the boundary between the side surface and the bottom surface that are in close contact with each other is point Q _{n, i, j, 1} and then, the line segment _{Q n, i, j, 0} Q n, i, j, 1 on the point Q _{n, i, j,} 2 points from closer to _{0 Q n, i, j,} 2 , Q _{n, i, j, 3} and line segments V _{n, i, j} Q _{n, i, j, 0} , Q _{1, i, j, 1} Q _{2, i, j, 1} are valley fold lines, Line segment Q _{n, i, j, 0} Q _{n, i, j, 2} , V _{n, i, j} Q _{n, i, j, 1} is a mountain fold line, line segment V _{n, i, j} Q _{n, i For, j, 2} and the line segment V _{n, i, j} Q _{n, i, j, 3} , one of them is a mountain fold line and the other is a valley fold, and the line segment Q _{n, i, j, 2} Q _{n , I, j, 1} can be provided with slits (linear cutting) (n = 1,2; i = 1,2; j = 1,2).
However, if the wall side surface V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i, 1} is missing, the vertices V _{1, i, 1} , V _{1, i, 2} , V ₂ It is not necessary to provide this configuration for _{, i, 2} , V _{2, i, 1 (i = 1, 2).}

Configuration 2 is a wall side surface V _{1, i, 1} V _{1, i, 2} V _{2, i} adjacent to the bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1. Let P n, i} be the intersection _{of the ridgeline of 2, 2} V _{2, i, 1} and the folding axis AX n (n = 1, 2, i = 1, 2), and the line segment P _{n, 1} P _{n in the bottom surface.} Two parallel line segments are provided on both sides of _{, 2 at an equal distance t 0} , and the end point of the parallel line segment closest to the vertices V _{n, i, j} is Z _{n, i, j} , and the end point Z _{n, i , J} coincides with the points Q _{n, i, j, 0} (n = 1, 2, i = 1, 2, j = 1, 2), and the line segments Q _{n, i, 1,0} Q _{n, i, Let S n, i, 0} be the intersection of _2,0 and the line segment P _{n, 1} P _{n, 2 , and the ridgeline V n, i, 1} V of the boundary between the side surface and the bottom surface of the wall that is closest to the intersection S _{n, i, 0.} n, i, 2 Let the foot of the perpendicular line drawn on _{n, i, 2 be the point S n, i, 1} (n = 1, 2, i = 1, 2), and the line segment S _{n, i, 0} S _{n, i in the bottom surface. , 1} , Z _{n, 1, j} Z _{n, 2, j} are set as valley fold lines, and _{slits are provided in the line segments Q n, i, 1, k} Q _{n, i, 2, k} (n = 1, 2,; i = 1,2; k = 0,1), and the line segment S1 _{, i, 1} S2 _{, i, 1} can be a mountain fold line (i = 1,2; j = 1,2). ..

However, if one or both of the wall side wall side V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i, 1} is missing and the configuration I is not provided, Z _{n, i, j} can be the intersection of the parallel line and the ridge line V _{n, i, 1} V _{n, i, 2.}

In the configuration 3, parallel lines are provided in the wall side surface at a distance t _{1 with respect to the ridge lines V 1, i, j} V _{2, i, j at} the boundary between the wall side surface and the lid side surface, and two points are provided on the line. Let the points close to the vertices V _{1, i, j} , V _{2, i, j be R 1, ij} , R _{2, i, j} , respectively. Here, the line segment R _{1, ij} R _{2, ij} is a valley fold line, _{and slits are provided in the line segments V 1, i, j} R _{1, ij} , V _{2, i, j} R _{2, ij} (i = 1, 2). ; J = 1, 2) can be done.

However, if either one or both of the bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1} is missing and the configuration I is not provided, a point R _{n, i, j} is the intersection of the parallel line and the ridge line V _{n, i, j} Q _{n, i, j, 1} , and no slit is provided in the line segment V _{n, i, j} R _{n, i, j.} It can be (n = 1,2; i = 1,2; j = 1,2).

The hollow polygonal columnar structure of the present invention can be folded without deforming the surface by rotating the surface around each ridge line and each polygonal line.

It is a developed view which shows an example of the hollow polygonal columnar structure by this invention. It is a schematic diagram for demonstrating composition I. It is a schematic diagram for demonstrating configuration II. It is a schematic diagram for demonstrating configuration II. It is a schematic diagram for demonstrating composition III. It is a schematic diagram for demonstrating the example which divides the bottom surface of a pentagon into two quadrangles. It is a schematic diagram for demonstrating the example which divides the bottom surface of an octagon into two quadrangles. It is a developed view which shows an example of the hollow square columnar structure of this invention. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a developed view which shows an example of the hollow pentagonal prism structure of this invention. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a perspective view which shows the compression process of the hollow square columnar structure of FIG. It is a developed view which shows an example of the hollow prism structure to which this invention is applied.

The hollow polygonal column structure of the present invention can be folded without deforming the surface by the rotation of the surface around each ridge line and each polygonal line.

The hollow quadrangular columnar structure 10 to which the present invention is applied is, as an example, a quadrangular columnar hollow structure as shown in the developed view in FIG. 1, and the shape of the bottom surface of one of them is a general quadrangle and The shapes of the opposite bottom surfaces are congruent. More specifically, congruent square V _1,1,1 V _1,2,1 V _1,2,2 V _1,1,2 and square V _2,1,1 V _2,2,1 V _2,2 Between the first and second end walls 12, 14 extending along the two bottom surfaces of a quadrangular prism having _{, 2} V _{2,1,2 as the bottom surfaces facing in parallel, and the two bottom surfaces.} It is a hollow structure including first to fourth side walls 16 to 22 extending along four side surfaces extending perpendicular to the bottom surface. The first and second end walls 12, 14 and the first to fourth side walls 16 to 22 are members made of flat plates, but may have irregularities or textures on their surfaces.

Further, the internal angles 2α _{i, j} (i = 1,2; j = 1,2) _{around the vertices V n, i, j} in the bottom surface forming the first and second end walls 12, 14 are α. _1,1 + α _1,2 + α _2,1 + α _2,2 = 180 ° and 0 ° <α _{i, j} <90 ° (i = 1,2; j = 1,2) It can be set freely and may be a non-isometric quadrangle. Further, the square columnar structure of the present invention may have an opening lacking a part of a surface, if necessary.

_{A pair of opposite sides V n, 1,1} V _{n, 2} , 1, V _{n, 1,} among the sides constituting the first and second end walls 12 and 14 of the hollow square columnar structure 10 of the present invention. ₂ V _n, the intersection when the extended each _2,2 (n = 1,2) and O _n. In the present invention, the _{angle formed by the extension lines of the sides V n, 1,1} V _{n, 2,1} , V _{n, 1,2} V _{n, 2,2} (n = 1, 2) at the O point is bisected. The straight line to be formed is referred _{to as "folding axis AX n".} The present invention folds _{the first and second end walls 12, 14 along the folding axis AX n,} and accordingly folds the two side walls 18, 22 connected to the first and second end walls 12, 14. The method.

When a pair of sides V _{n, 1,1} V _{n, 2,1} , V _{n, 1,2} V _{n, 2,2} (n = 1, 2) are parallel, they are parallel to two sides equidistant from the two sides. Straight line becomes the folding axis. In the present specification, the side walls 18 and 22 "wall side surfaces" that are folded together with the first and second end walls 12 and 14, and the side walls 16 and 20 that move with the deformation of the end walls without themselves being folded. It is called "the side of the lid". In the following description, the surfaces forming the first and second end walls 12 and 14 are referred to as bottom surfaces.

In the present invention, the following three configurations are introduced in order to realize the above folding. Configuration I: Folding configuration at the boundary region between the bottom surface and the side surface of the wall. Configuration II: A configuration that eliminates surface interference due to folding in the boundary area between the side surface of the lid and the side surface of the wall. Configuration III: A configuration that eliminates surface interference due to folding along the folding line at the center of the bottom surface and the side surface of the wall.

The configuration I is a configuration in which the length of the slit near the ridgeline of the bottom surface and the wall surface required by the "bellows theory" is reduced by additionally introducing a specific polygonal line. In configurations II and III, when folding a quadrangular prism consisting of rigid bodies with a finite thickness, the thickness of the plates additionally identifies the inhibition of folding deformation due to positional interference between the plates as a specific folding line. A slit with a limited length is introduced, and the problem is solved by using the hinge shift method. In the hinge shift method, all surfaces are cut once with fold lines, and the hinges are installed and joined at the valley folds corresponding to each fold line. Is only offset.

Further, as a further method, a method of joining the surfaces on both sides of the polygonal line with a hinge at a finite distance is performed, and the thickness is increased by introducing an additional polygonal line and a slit which are exactly the same as the hinge shift method. The effect can be avoided. This is hereinafter referred to as the isotropic hinge method.

When the square columnar structure is a completely closed structure, that is, the walls are provided on all surfaces, the configuration I needs to be provided on the boundary region between all the bottom surfaces and the side surfaces of the walls. In a hollow square columnar structure having an opening surface lacking a wall side surface, it is not necessary to provide the configuration I at the boundary between the opening surface and the bottom surface. Unless one of the bottom surfaces is not chipped, the shapes of the configurations I on both bottom surfaces need to be congruent and have the same direction. The configuration of the configuration II changes depending on whether the configuration I is provided or not. If the side surface of the lid is missing, there is no change in the configurations I to III except that each side of the side surface of the lid does not form a polygonal line.

Each configuration will be further described below.
_{Below, the bottom surface V n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2,1} (n = 1, 2) of the congruent quadrangle shown in FIG. 1 _{is the two wall side surfaces V 1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i, 1} (i = 1, 2) and two lid sides V _{1,1, j} V _{1,2, j} V _{2,2, Consider a quadrangular columnar structure connected by j} V _{2,1, j} (j = 1, 2). Ridge line V _{n, 1, j} V _{n, 2, j} (n = 1, 2, j = 1, 2,), V _{1, i, j} V _{2, i, j} (i = 1, 2, j = 1, The polygonal line corresponding to 2) is defined here as a mountain fold line. That is, the fold line convex to the outside of the tetrahedral structure is referred to as a mountain fold line. The hollow square columnar structure may lack one or two of the six surfaces constituting the hollow square columnar structure. When the intersection of the internal angle bisectors around the two vertices V _{n, i, 1} , V _{n, i, 2 in each bottom surface is C n, i} , connect the intersections C _{n, 1} , C _{n, 2.} The straight line _{coincides with the folding axis AX n} (n = 1,2; i = 1,2).

Configuration I
Referring to FIG. 2, for the vertices V _{n, i, j} constituting the bottom surface, an isometric bisector of the internal angle 2α _{i, j in} the bottom surface is drawn from the _{vertices V n, i, j,} and the bisector is drawn in the bottom surface. Set the end points Q _{n, i, j, 0} . From the end point Q _{n, i, j, 0} , point the foot of the perpendicular line drawn on _{the ridgeline V n, i, 1} V _{n, i, 2} of the boundary between the side and bottom of the wall that is in close contact _{with the point Q n, i, j, 1} Then, on the line segment Q _{n, i, j, 0} Q _{n, i, j, 1} , two points from the closest to the point Q _{n, i, j, 0 Q n, i, j, 2} , Q _{n, i Take, j, 3} . Line segment V _{n, i, j} Q _{n, i, j, 0} , Q _{1, i, j, 1} Q _{2, i, j, 1} is a valley fold line, line segment Q _{n, i, j, 0} Q _{n , i, j, 2} , V _{n, i, j} Q _{n, i, j, 1} is a mountain fold line, line segment V _{n, i, j} Q _{n, i, j, 2} and line segment V _{n, i, For j} Q _{n, i, j, 3} , one of them is a mountain fold line and the other is a valley fold line, and the line segments Q _{n, i, j, 2} Q _{n, i, j, 1} are slit (line). (Shaped cutting) is provided (n = 1,2; i = 1,2; j = 1,2).

If the wall side V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i, 1} is missing, the vertices V _{1, i, 1} , V _{1, i, 2} , V _{2, i , 2} , V _{2, i, 1} need not have the above configuration I. (I = 1, 2)

Configuration II
In FIG. 3, the bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1,} and the adjacent wall side surfaces V _{1, i, 1} V _{1, i, 2} V _{2, Let P n, i} be the intersection _{of the ridgeline of i, 2} V _{2, i, 1} and the folding axis AX n (n = 1, 2, i = 1, 2). Two parallel line segments are provided on both sides of the line segment P _{n, 1} P _{n, 2 at} an equal distance t ₀ in the bottom surface, and the end point of _{the parallel line segment close to the vertices V n, i, j is Z n. , I, j} (Fig. 4), and the end points Z _{n, i, j} coincide with the points Q _{n, i, j, 0} (n = 1, 2, i = 1, 2, j = 1, 2).

Furthermore, the intersection of the line segment Q _{n, i, 1,0} Q _{n, i, 2,0} and the line segment P _{n, 1} P _{n, 2 is set to S n, i, 0} , and the intersection S _{n, i, 0 is the} latest. Let the foot of the perpendicular line drawn on _{the ridge line V n, i, 1} V _{n, i, 2} of the boundary between the side surface and the bottom surface of the wall in contact be the _{point S n, i, 1} (n = 1, 2; i = 1, 2). ). At this time, the line segments S _{n, i, 0} S _{n, i, 1} , Z _{n, 1, j} Z _{n, 2, j} are set as valley fold lines in the _{bottom surface, and the line segments Q n, i, 1, k} Q _{n , I, 2, k} are provided with slits (n = 1, 2, i = 1, 2, k = 0, 1), and the line segments S _{1, i, 1} S _{2, i, 1} are defined as mountain fold lines. (I = 1,2; j = 1,2). Wall side wall side _{V 1, i, 1 V 1} , i, 2 V 2, i, 2 V 2, i, 1 in the case where any one or constructed lacked both I was not provided endpoint Z _{n , i, j} are the intersections of the parallel lines and the ridges V _{n, i, 1} V _{n, i, 2.}

Configuration III
In FIG. 5, parallel lines are provided in the wall wall surface at _{a distance of t 1 with respect to the ridge lines V 1, i, j} V _{2, i, j at} the boundary between the wall side surface and the lid side surface, and two points are scored on the lines. Let the points close to the vertices V _{1, i, j} , V _{2, i, j be R 1, ij} , R _{2, i, j} , respectively. Here, the line segment R _{1, ij} R _{2, ij is provided} with a valley fold line, and the line segments V _{1, i, j} R _{1, ij} , V _{2, i, j} R _{2, ij} are provided with slits. (I = 1,2; j = 1,2). If one or both of the bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1} is missing and the configuration I is not provided, the point R _{n, i, j} is the intersection of the parallel line and the ridge line V _{n, i, j} Q _{n, i, j, 1} , and no slit is provided in the line segment V _{n, i, j} R _{n, i, j} (n = 1,). 2; i = 1,2; j = 1,2).

_{The thickness of the bottom surface V n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2,1} of the tetrahedral structure of the present invention is T _{n, b} (n = 1, 2), When the thickness of the wall side surface V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i, 1 is Ti, w} (i = 1, 2), the distance t of the present invention _{It is necessary for 0} and t ₁ to satisfy the following conditions at the same time.

Here, the distance between arbitrary points A and B is represented by L (A, B), U ₁ = L (P _1,1,0 , P _1,1,1 ), U ₂ = L (P _{1, It} is defined as 2,0, _P1,2,1). In the above equation, at distances t ₀ and t ₁ below the lower limit, folding can only be achieved incompletely or cannot be folded at all due to interference of surface thickness. In addition, if the upper limit is exceeded, the stability of the structure will be lost due to the geometrical formation limit of the prismatic structure.

When the thickness of the square columnar structure is extremely thin and there is virtually no influence of the thickness, t ₀ = 0 and t ₁ = 0. _{Q n, i, 1, k} and Q _{n, i, 2} and S _n when the configuration I is provided without providing two parallel line segments on both sides of the line segments P _{n, 1} P _{n, 2. , I, k} match (n = 1,2; i = 1,2; k = 0,1), and points Q _{n, i, 1, k} , Q _{n, i, 2, k} match (n = 1, 2, k) n = 1,2; i = 1,2: k = 2,3). If the configuration I is not provided, the end points Z _{n, i, 1} and Z _{n, i, 2} coincide with the intersection P _{n, i} (n = 1, 2; i = 1, 2).

Further, when determining the points R _{n, i, j} (n = 1, 2, i = 1, 2, j = 1, 2) of the present invention, it is preferable to satisfy the following conditions.
Q _{n, i, j, 1} V _{n, i, j} R _{3-n, i, j} ＞ ∠ Q _{n, i, j, 1} V _{n, i, j} R _{n, i, j} ≧ α _{i, j} ( n = 1,2; i = 1,2; j = 1,2)

In the above equation, the lower limit can only be incompletely folded or cannot be folded at all at angles below it due to surface thickness interference. In addition, if the upper limit is exceeded, the stability of the structure will be lost due to the geometrical formation limit of the prismatic structure.

Ratio of lengths of polygonal lines Q _{n, i, j, 0} Q _{n, i, j, k} (n = 1,2; i = 1,2; j = 1,2; k = 2,3) of the present invention It is preferable that both of the following conditions are satisfied with respect to g (hereinafter, line segment ratio).
0 <g _{n, i, j, 3} <0.83
g _{n, i, j, 3} <g _{n, i, j, 3} <0.95
Here, g _{n, i, j, i} = L (Q _{n, i, j, 0} , Q _{n, i, j, k} ) / L (Q _{n, i, j, 0} , Q _{n, i, j, 1} ) (n = 1,2; j = 1,2; k = 2,3).

In the above equation, if the upper limit is exceeded, the geometrical constraint condition that comes from the "bellows principle" cannot be avoided, and folding is only incompletely realized or cannot be folded at all. .. The range of more preferable line segment ratios g _{n, i, j, 3} , g _{n, i, j, 3} (n = 1, 2, i = 1, 2, j = 1, 2) is shown by the following equation. Is done.
0.5 <g _{n, i, j, 3} <0.83 and g _{n, i, j, 3} <gn _{, i, j, 3} <0.93

Since the line segment ratio g _{n, k, 2} (n = 1,2; k = 1,2,3,4) is 0.5 or more, the cutting amount (slit length) can be reduced. More preferred.

In the present invention, when a quadrangular prism is completely folded, if the thickness of each surface is the same, it can be compressed to a thickness eight times the thickness of the surface in a substantially completely folded state. Therefore, the effect of contributing to the compactness of the structure is extremely high. In addition, the slits on the ridgeline can be minimized, and the completeness of the structure as a square pillar in the unfolded state is not significantly impaired.

In the present invention, the shape of the bottom surface (two opposing end walls) is not limited to a quadrangular one, and for a polygonal pillar having an arbitrary polygonal bottom surface, this is divided into a plurality of quadrangular prisms, and the divided individual pillars are divided. By performing the same operation on the quadrangular prismatic structure of, the whole can be folded substantially completely. Figures 6 and 7 show examples of such bottom surface division.

FIG. 6 shows a case where the bottom surface (two opposing end walls) is pentagonal. In FIG. 6, the wall forming the pentagonal bottom surface 50 is divided into two quadrangles 52 and 54 by the dividing line indicated by the broken line BL, and is compressed in the directions of _{arrows D 1} and D _{2, respectively.}

FIG. 7 shows a case where the bottom surface (two opposing end walls) is octagonal. In FIG. 7, the wall forming the octagonal bottom surface 60 is divided into three quadrangles 62, 64, 66 by _{the broken lines BL 1} and BL ₂ , and is compressed in the directions of _{arrows D 1} , D ₂ , and D _{3, respectively.} ..

Dividing lines BL; BL ₁ and BL ₂ are provided so that they do not intersect each other and multiple dividing lines do not share vertices. Dividing line BL; _{The starting points of BL 1} and BL ₂ do not necessarily have to be vertices, and can be set to any point on the ridgeline. The opposite bottom surfaces (end walls) must have exactly the same dividing line BL; BL ₁ and BL ₂ patterns, and can be cut by cutting a polygonal prism on a plane that includes the corresponding dividing lines on both bottom surfaces. It can be divided into hollow square columnar structures lacking the side surface of the lid corresponding to the surface. By applying the above-mentioned configurations I to III to the hollow square columnar structure and _{joining the dividing lines BL; BL 1} and BL ₂ as mountain fold lines, a polygonal columnar structure that can be folded is obtained.

In the present invention, a square columnar structure is constructed by cutting a surface along all the above-mentioned ridge lines, fold lines and slits by a hinge shift method and joining the surfaces with a hinge on the surface of Tanigawa at each fold line portion. In this case, in the state of not folding at all, each surface can be in complete contact without a gap.

An isotropic hinge method can also be used in the present invention. The isotropic hinge method is a method of joining polygonal lines with a flexible material having a finite width. Width t of this time isotropic hinge ', the thickness of the two walls to be joined at the hinge (face) each T' it is necessary that the following conditions are satisfied when a _1, T _{'2.
T '1 + T' 2 <} t '

When the width t'of the hinge falls below this lower limit, it becomes impossible to completely bend the two surfaces to which it joins with an isotropic hinge.
A more preferable range of the hinge width t'can be expressed by the following equation.
(T ′ ₁ + T ′ ₂ ) × 1.5 <t ′ <(T ′ ₁ + T ′ ₂ ) × 100

The joining position of the isotropic hinge and the face may be between the two walls (faces) joined by the isotropic hinge and the surface of the face on the valley fold side or the mountain fold side.
The hinge shift method and the isotropic hinge method may be mixed and used in the same structure.

The material of the wall (face) constituting the polygonal columnar structure used in the present invention is not particularly limited, but is not particularly limited, but is limited to metal materials such as iron and aluminum, plastics, ceramics, paper, inorganic porous materials, and organic porous materials. , A fiber-reinforced composite material, a sandwich material composed of a fiber-reinforced composite material and a porous material, and the like can be used. In particular, when portability and mobility are utilized, it is preferable to use a fiber-reinforced composite material, a sandwich material composed of a fiber-reinforced composite material and a porous material, because it has both structural rigidity / strength and light weight.

As the hinge used in the present invention, a general metal hinge or a resin hinge that is mechanically or adhesively fastened, or a hinge to which a flexible wall (face) material is attached can be used. As the material of the flexible wall (face), a paper material capable of large deformation, a fiber material such as a woven fabric or knitting, a rubber, an elastic resin, a paper material or a composite of a fiber material and an elastic resin, etc. should be used. Can be done. In particular, when a fiber-reinforced resin composite material is used as the material for the wall (surface), it is preferable to apply the isotropic hinge method using an FRP hinge.

The FRP hinge is a hinge made of a plate material made of a fiber-reinforced resin composite material by forming a region in which a matrix resin is substantially absent in a straight line and impregnating a flexible resin as it is or instead of the matrix resin. It is a thing. When an FRP hinge is formed using a composite material reinforced with continuous fibers as a plate material, high strength and durability can be expected because the fibers are continuous between the plate material and the hinge portion, and the hinge portion is continuous with respect to the entire broken line. ..

As the resin used for the FRP hinge, a composite of elastic resins such as silicone rubber, olephine-based elastomer, and fluororesin-based elastomer is more preferable from the viewpoint of durability and sealing property. When a highly deformable elastic resin is used, the slit required in the above configuration may be replaced with a hinge, and a structure having high watertightness and airtightness can be obtained.

Each surface of the polygonal columnar structure obtained in the present invention does not necessarily have to be a completely closed structure, and an opening can be arbitrarily provided in a part of the surface.
Further, the polygonal columnar structure of the present invention can be used not only alone but also by connecting a plurality of the polygonal columnar structures by a method such as merging.

Since a plate material having an arbitrary thickness can be applied to the folding structure of the present invention, it is possible to provide a folding structure having excellent mechanical properties. In addition, by being substantially completely foldable, it becomes compact and highly efficient for transportation and storage. From these characteristics, the present invention can be effectively applied to mobile simple houses, temporary stores for events, temporary buildings such as portable toilets, air containers, general transportation containers, and the like.

FIG. 8 is a developed view showing an example of the hollow square columnar structure of the present invention, and FIGS. 9 to 14 are compression processes of the hollow square columnar structure 70 shown in a perspective view. In FIGS. 8 to 14, the hollow square columnar structure 70 has an end wall 72 forming one of the bottom surfaces of congruent quadrangles facing each other, side walls 74 and 76 forming the wall side surface, and side wall 78 forming the lid side surface. , 80, and the end wall 72 is folded with the folding axis AX as a valley fold line. In this example, the end wall facing the end wall 72 is not provided, and the other bottom surface is open.

FIG. 15 is a developed view showing an example of the hollow pentagonal prism structure of the present invention, and FIGS. 16 to 21 are compression processes of the hollow pentagonal prism structure shown in a perspective view. In FIGS. 15 to 21, the hollow square columnar structure 100 has an end wall 102 forming one of the bottom surfaces of congruent quadrangles facing each other, side walls 104 and 106 forming the side surface of the wall, and side wall 108 forming the side surface of the lid. , 110 and. In this example, the end wall facing the end wall 102 is not provided, and the other bottom surface is open.

The end wall 102 is divided into end wall portions 112 and 114 by a dividing line BL. The side wall 104 has a side wall portion 116 connected to the end wall portion 112 and a side wall portion 118 connected to the end wall portion 114. The side wall 106 has a side wall portion 120 connected to the end wall portion 112 and a side wall portion 122 connected to the end wall portion 114. The end wall 102 is folded with the folding axes AX ₁ and AX ₂ as valley fold lines.

I made a development view of a rectangular parallelepiped that can be folded by the following procedure.
_{Ridge line V n, i, 1} V _{n, i, 2} (n = 1, 2; i = 1, 2) with a length of 300 mm, ridge _{line V n, 1, j} V _{n, 2, j with a length of 1000 mm} Development view of a rectangular parallelepiped consisting of (n = 1,2; j = 1,2) and a ridgeline V _{1, i, j} V _{2, i, j (i = 1, 2, j = 1, 2,) having a length of 300 mm.} It was created.

With respect to the developed view of the rectangular parallelepiped, the two vertices V _{n, i, 1} , V _{n, i, with respect to the bottom surface V n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2,1} The intersection of the bisectors of the internal angle drawn from _{2 is C n, i} , and the foot of the perpendicular line drawn _{from the intersection C n, i} to the ridges V _{n, i, 1} , V _{n, i, 2 is S n, i, It was set to 1} (n = 1,2; i = 1,2). Further, parallel lines are provided on both sides of the line segments C _{n, 1} C _{n, 2 at a distance of 9 mm, and the intersections of the parallel lines and the line segments V n, i, j} C _{n, i} are set to Q _{n, i, j, 0} , the foot of the parallel line drawn from the intersection Q _{n, i, j, 0} to the ridgeline V _{n, i, 1} V _{n, i, 2 is Q n, i, j, 1} , and the line segment Q _{n, i, j On, 0} Q _{n, i, j, 1} the line segment ratio g _{n, i, j, 3} is 0.60, and the line segment ratio g _{n, i, j, 3} is 0.83. Two points Q _{n, i, j, 2} and Q _{n, i, j, 3} (n = 1,2; i = 1,2; j = 1,2) were taken so as to be. The intersection of the line segment Q _{n, i, 1,0} Q _{n, i, 2,0} and the straight line connecting _{the intersection C n, i} and the perpendicular foot S _{n, i, 1 is S n, i, 0.} (N = 1,2; i = 1,2).

Ridgeline _{V 1, i, j V 2} , i, take two different points in the parallel lines provided at a distance of 8mm in the wall side containing contrast _j, vertex V _{1, i,} a point close to the _j The _{points close to R 1, i, j} and the vertices V _{2, i, j} were designated as R _{2, i, j} (i = 1, 2; j = 1, 2). At this time, the angle ∠Q _{n, i, j, 1} V _{n, i, j} R _{n, i, j} (n = 1,2; i = 1,2; j = 1,2) was set to 45 °.

Lines V _{n, i, j} Q _{n, i, j, k} , Q _{n, i, j, 0} Q _{n, i, j, 2} , R _{1, i, j} R _{2, i, j} , S _{n, Let i, 0} S _{n, i, 1} (n = 1,2; i = 1,2; j = 1,2; k = 1,3) be a mountain fold line, and the line segment V _{n, i, j} Q _{n , i, j, k} , Q _{1, i, j, 1} Q _{2, i, j, 1} , S _{1, i, 1} S _{2, i, 1} , Q _{n, 1, j, 0} Q _{n, 2, Let j, 0} (n = 1,2; i = 1,2; j = 1,2; k = 0,2) be a valley fold line, and the line segments Q _{n, i, j, 2} Q _{n, i, j , 1} , V _{n, i, j} R _{n, i, j} (n = 1,2; i = 1,2: j = 1,2) were used as slits.

According to the above developed view, a styrofoam board having a thickness of 3 mm is cut into wall (face) elements by cutting faces at all ridges and fold lines, and each cut wall (face) element is used as a board on the valley fold side of each fold line. A rectangular parallelepiped hollow structure was created by joining the surfaces with flexible plastic tape. Ridge lines V _{n, 1, j} V _{n, 2, j} (n = 1, 2, j = 1, 2,), V _{1, i, j} V _{2, i, j} (i = 1, 2, j = 1) , 2) were joined in the same way as a mountain fold. At this time, the portion corresponding to the slit was not joined.

The obtained rectangular parallelepiped hollow structure could be completely folded and compressed to a height of 25 mm. In addition, it was possible to repeatedly change the shape between rectangular parallelepiped shapes from this completely compressed state.

Ridge line V _{n, 1,1} V _{n, 1,2} , V _{n, 1,2} V _{n, 2,2} , V _{n, 2,1} V _{n, 2,2} , V _{n, 1,1} V _{n, The lengths of 2,1} (n = 1,2) are 300 mm, 700 mm, 424 mm, and 1000 mm, the lengths of the ridges V _{1, i, j} V _{2, i, j} are 300 mm, and the internal angle 2α _{1,1 ,, 2α 1,2, 2α 2,1,} 2α 2,2 to 90 °, 90 °, 45 ° , and 135 °, the angle _{∠Q n, 2,1,1 V n, 2,1} R n, 2 _{, 1} (n = 1, 2) is 22.5 °, and the angle ∠Q _{n, 2,2,1} V _{n, 2,2} R _{n, 2,2} (n = 1, 2) is 70 °. A square columnar hollow structure having a trapezoidal bottom surface was prepared in exactly the same manner as in Example 1 except for the above. The obtained rectangular parallelepiped hollow structure could be completely folded and compressed to a height of 25 mm. Moreover, from this completely compressed state, it was possible to repeatedly change the shape between the rectangular parallelepiped shapes.

A hollow square with one side open in exactly the same way as in Example 1 except that the lid side surface V _1,1,2 V _1,2,2 V _2,2,2 V _{2,1,2 is missing.} create a columnar structure, also except that lacks a lid side _{V 1,1,1 V 1,2,1 V 2,2,1 V 2,1,1} , exactly the same manner as in example 2 Then, a hollow square columnar structure with one side open was created, and the ridgelines of the hollow square columnar structure V _1,2 V _1,3 , V _1,3 V _2,3 , V _2,3 V _2,2 , V _2,2 V _1,2 are the ridges of the hollow square columnar structure V _1,1 V _1,4 , V _1,4 V _2,4 , V _2,4 V _2,1 , V _2,1 V _{1 A pentagonal columnar hollow structure was created by joining each of 1 and 1} with a flexible plastic tape on the inside so that the outside of the hollow structure would form a mountain fold.

The obtained rectangular parallelepiped hollow structure could be completely folded and compressed to a height of 50 mm. In addition, it was possible to repeatedly change the shape from this completely compressed state to a rectangular parallelepiped shape.

Moreover, the present invention may be carried out with the following features.
[Feature 1]
In a square _{pillar composed of congruent quadrangles V 1,1} V ₁ , ₂ V ₁ , ₃ V ₁ , ₄ and quadrangles V _{2, 1} V ₂ , ₂ V ₂ , ₃ V ₂ , ₄ facing each other.
The intersection of the bisectors of the internal angles drawn from the _{two vertices V n, 2j-1} , V _{n, 2j} in the plane of the bottom surface V _{n, 1} V _{n, 2} V _{n, 3} V _{n, 4 is P n, Defined as j, 0} (n = 1,2; j = 1,2),
The foot of the perpendicular line drawn from the intersection P _{n, j, 0} to the line segment V _{n, 2j-1} V _{n, 2j is defined as P n, j, 1} (n = 1, 2; j = 1, 2).
The intersection of a straight line passing through two points P _{n, 1,0} , P _{n, 2,0} and a line segment V _{n, 2j-1} V _{n, 2j is defined as Z n, j, 0} (n = 1, 2, 0). J = 1,2),
Two different points are taken on the line segment P _{n, j, 0} P _{n, j, 1} , and the one close to the _{point P n, j, 1 is defined as P n, j, 2,} and the one far away is P _{n. When defined as, j, 3} (n = 1,2; j = 1,2), it is characterized by satisfying all of the following conditions, by rotation around each ridge and each polygonal line without deforming the surface. A foldable square columnar structure.
(1) _{Let the line segment V n, j} V _{n, 5-j} (n = 1, 2; j = 1, 2) be a mountain fold polygonal line.
(2) Line segments V _{n, 2j-1} V _{n, 2j} , P _{n, j, 0} P _{n, j, 1} are mountain folds, and line segments V _{n, k} P _{n, j, 0} are valley folds. the fold lines, the line segment V _{n, k} P _{n, j, 2} a line V _{n, k} P _{n, j, 3} of one mountain folding fold line, and the other as a polygonal line for valley fold, the point P _{n , J, 1} to line segments P _{n, j, 0} P _{n, j, 1} are provided with (slits) in all or part (n = 1, 2, j = 1, 2, k = 2j-1,2j ).
(3) P _{n, 1,0} P _{n, 2,0} (n = 1, 2) is a valley fold line.
(4) Let V _{1, k} V _{2, k} (k = j, 5-j; j = 1, 2) be a mountain fold fold line.
(5) P _{1, j, 1} P _{2, j, 1} (j = 1, 2) is a valley fold line.
[Feature 2]
A square columnar structure lacking one or both of the two facing sides V _1,1 V _1,4 V _2,4 V _2,1 , V _1,2 V _1,3 V _2,3 V _{2, 2.} Yes, the range of j of the conditions (1) and (4) described in the feature 1 is limited to j = 2 or j = 1, respectively, or if both sides are lacking, the conditions (1) and (4) are lacking. A square columnar structure with foldable openings, obtained in exactly the same manner as in Feature 1.
[Feature 3]
Facing bottom surface V _1,1 V ₁ , ₂ V ₁ , ₃ V ₁ , ₄ , V ₂ , 1 V ₂ , ₂ V ₂ , ₃ V ₂ , ₄ It is a square columnar structure lacking one of them, and feature 1 A square columnar structure with a foldable opening, which is obtained in exactly the same manner as in Feature 1, except that the range of n in the conditions (1) to (3) is limited to n = 2 or n = 1, respectively. ..
[Feature 4]
It is a square columnar structure lacking one of the side surface V _1,1 V _1,2 V _2,2 V _2,1 and the side surface V _1,3 V _1,4 V _2,4 V _{2,3, and has the feature 1.} Instead of the polygonal _{line P n, 1,0} P _{n, 2,0} of the condition (3), the polygonal _{line P n, 5-k, 0} Z _{n, k, 0} (n = 1, 2, j = 1, 2, k) = 2j-1,2j) is provided, and this and the condition (1) to (5) of feature 1 are obtained in exactly the same manner as feature 1 except that the range of j is limited to j = 2 or j = 1, respectively. A square columnar structure with a foldable opening.
[Feature 5]
When the length of the line segment P _{n, j, 0} P _{n, j, i is L (P n, j, 0} P _{n, j, i} ), the following equation is satisfied at the same time. The tetrahedral structure according to any one of 1 to 4.
0 <f _{n, j, 2} <0.83, f _{n, j, 2} <f _{n, j, 3} <0.92 (n = 1, 2; j = 1, 2)
Here, f _{n, j, i} = L (P _{n, j, 0} P _{n, j, i} ) / L (P _{n, j, 0} P _{n, j, 1} ). (N = 1,2; i = 2,3; j = 1,2)
[Feature 6]
Line segment P _{n, j, 0} P _{n, j, 1,} (n = 1, 2; j = 1, 2) When providing a cut (slit) for the line segment P _{n, j, 2} P _{n, j} The square columnar structure according to any one of features 1 to 5, wherein a cut is provided only at a portion of 1 _{, 1 (n = 1, 2; j = 1, 2).}
[Feature 7]
From a surface of finite thickness composed of congruent quadrilateral V _1,1 V ₁ , ₂ V ₁ , ₃ V ₁ , ₄ and quadrangle V _{2, 1} V ₂ , ₂ V ₂ , ₃ V ₂ , _{4 as the bottom surface} In the quadrangular pillars that are constructed
Bottom _{V n, 1 V n, 2} V n, 3 V n, 2 vertices V _n in the _{4, 2j-1, V n} , the intersection of P _n bisector of the interior angle drawn from _{2j, j, Defined as 0} (n = 1,2; j = 1,2),
The foot of the perpendicular line drawn from the point P _{n, j, 0} to the line segment V _{n, 2j-1} V _{n, 2j is defined as P n, j, 1} (n = 1,2; j = 1,2).
The intersection of a straight line passing through two points P _{n, 1,0} , P _{n, 2,0} and a line segment V _{n, 2j-1} V _{n, 2j is defined as Z n, j, 0} (n = 1, 2, 0). J = 1,2),
Parallel lines are provided on both sides of the line segment Z _{n, 1,0} Z _{n, 2,0 at a distance of t 0} , and the intersection of the parallel line and the line segment V _{n, k} P _{n, 1,0 is Q n, k, 0} , the intersection of the parallel line and the line segment V _{n, k} Z _{n, j, 0 is defined as Z n, j, k} (n = 1,2; j = 1,2; k = 1, 2,3,4),
The foot of the perpendicular line drawn from the point Q _{n, k, 0} to the line segment V _{n, k} P _{n, j , 1 is defined as Q n, k, 1} (n = 1, 2, j = 1, 2, k). = 2j-1,2j),
Two points are taken on the line segment Q _{n, k, 0} Q _{n, k, 1 , and the points close to Q n, k, 0} are close to Q _{n, k, 2} , Q _{n, k, 1.} Is _{defined as Q n, k, 3} (n = 1,2; j = 1,2; k = 2j-1,2j).
The intersection of the line segment Q _{n, 2j-1,0} Q _{n, 2j, 0} and the line segment P _{n, j, 0} P _{n, j, 1 is defined as S n, j} (n = 1, 2, j). = 0,1),
Relative line _{V 1, k V 2, k} , parallel lines and the line segment V ₁ provided at a distance of t ₁ in side containing _{it, k} Q _{1, k,} 1 and line V _{2, k} Q The intersections of _{2, k and 1 are defined as Y 1, k} and Y _{2, k} , respectively (k = 1, 2, 3, 4).
Two different points are taken on the line segment Y _{1, k} Y _{2, k} , and the points close to _{Y 1, k are defined as R 1, k} , and the points close to _{Y 2, k are defined as F, k} (k). = 1,2,3,4),
The internal angles around the tops V _{1, k} and V _{2, k of the bottom surface are 2 α k} (k = 1 _{, 2, 3, 4)} , and the thickness of the _{bottom surface V n, 1} V _{n, 2} V _{n, 3} V n, 4. is but _{T b, n (n = 1,2} ), side _{V 1,2j-1 V 1,2j V 2,2j} V 2,2j-1 having a thickness of _{T l, j (j = 1,2} ) When, a quadrangular columnar structure that can be folded by rotation around a ridge and a fold line without surface deformation, characterized in that it satisfies all of the following conditions with respect to the quadrangular columnar structure.
(1) _{Let the line segments V n, j} V _{n, 5-j} be mountain fold polygonal lines. (N = 1,2; j = 1,2)
(2) Line segment V _{n, k} Q _{n, k, 1} , Q _{n, k, 0} Q _{n, k, 1} , S _{n, j} P _{n, j, 1} is a mountain fold fold line, line segment V _{n, k} Q _{n, k, 0} is the valley fold fold line, line segment V _{n, k} Q _{n, k, 2} and any of the line segments V _{n, k} Q _{n, k, 3} is the valley fold fold line, the other is the mountain fold Make a fold line and _{cut it into line segments Q n, 2j-1, i} Q _{n, 2j, i} , from point Q _{n, k, 1} to part of line segment Q _{n, k, 0} Q _{n, k, 1} . All are provided with slits (n = 1,2; i = 0,1; j = 1,2; k = 2j-1,2j).
(3) _{Let the line segment Q n, j, 0} Q _{n, 5-j, 0} (n = 1, 2; j = 1, 2) be a valley fold polygonal line.
(4) Line segments R _{1, k} R _{2, k} are mountain-folded polygonal lines, and _{slits are provided in V n, k} R _{n, k} (n = 1, 2, j = 1, 2, k = 2j-1). , 2j).
(5) Let the line segments V _{1, k} V _{2, k} be mountain fold polygonal lines (j = 1, 2; k = j, 5-j).
(6) P _{1, j, 1} P _{2, j, 1} is a mountain fold fold line, and line segments Q _{1, k, 1} Q _{2, k, 1} are valley fold fold lines (j = 1, 2,; k = j, 5-j).
(7) t ₀ and t ₁ satisfy the following conditions at the same time.
2 × max {T _ln ; (n = 1, 2)} + max {T _bn ; (n = 1, 2)} <t ₀ <min {Un _{, k cosα j} / sinα _3-j ; (n = 1) , 2; k = 1,2; j = 1,2)}
max {T _bn ,; (n = 1, 2)} <t ₁ <min {L (V _{n, k} Q _{n, k, 1} ); (n = 1, 2, k = 1, 2, 3, 4) )}
Here, it is assumed that _{Un, k} = L (P _{n, k, 0} P _{n, k, 1} ) (n = 1,2; k = 1,2).
[Feature 8]
A square columnar structure lacking one or both of the side V _1,1 V _1,4 V _2,4 V _2,1 and the side V _1,2 V _1,3 V _2,3 V _{2, 2.} The range of j in the conditions (1) and (4) of the feature 7 is limited to j = 2 or j = 1, respectively, or if both sides are lacking, the condition (1) and (4) are lacking. A square columnar structure with foldable openings, obtained in exactly the same way.
[Feature 9]
_{It is a square columnar structure lacking one of} the bottom surface V _1,1 V _{1, 2} V ₁ , ₃ V ₁ , ₄ and the bottom surface V _{2, 1} V ₂ , ₂ V ₂ , ₃ V ₂ , ₄ , and the condition of feature 7. A square column with a foldable opening obtained in exactly the same manner as in Feature 7, except that the range of n in (1)-(4) and (7) is limited to n = 2 or n = 1, respectively. Structure.
[Feature 10]
It is a square columnar structure lacking one of the side surface V _1,1 V _1,2 V _2,2 V _2,1 and the side surface V _1,3 V _1,4 V _2,4 V _{2,3, and has the feature 7.} Polygonal line Q _{n, j, 0} Q _{n, 5-j, 0} instead of the polygonal line Q _{n, 5-k, 0} Z _{n, k, 0} (n = 1, 2; j = 1, 2) ; K = 2j-1,2j) is provided, and the range of j in the feature 7 conditions (1) to (2) and (4) to (6) is limited to j = 2 or j = 1, respectively. A square columnar structure with a foldable opening, obtained in exactly the same manner as in Feature 7.
[Feature 11]
The square columnar structure according to any one of features 7 to 10, wherein when determining points R _{1, k} and points R _{2, k, the following conditions are satisfied.}
Q _{n, k, 1} V _{n, k} R _{3-n, k} ＞ ∠ Q _{n, k, 1} V _{n, k} R _{n, k} ≧ α _k (n = 1, 2, k = 1, 2, 3, 4).
[Feature 12]
The square columnar structure according to any one of features 7 to 11, characterized in that the following conditions are simultaneously satisfied with respect to the lengths of the line segments Q _{n, k, 0} Q _{n, k, i.}
0 <g _{n, k, 2} <0.83, g _{n, k, 2} <gn _{, k, 3} <0.92
Here, g _{n, k, i} = L (Q _{n, k, 0} Q _{n, k, i} ) / L (Q _{n, k, 0} Q _{n, k, 1} ). (N = 1,2; k = 1,2,3,4; i = 2,3)
[Feature 13]
When providing slits in part or all of the line segments Q _{n, k, 1} Q _{n, k, 0} (k = 1, 2, 3, 4), Q _{n, k, 1} Q _{n, k, 2} (k) = The square pillar structure according to any one of features 7 to 12, characterized in that slits are provided only in the portions 1, 2, 3, 4).
[Feature 14]
Item 2. Foldable square columnar structure.
[Feature 15]
The square columnar structure according to any one of features 7 to 13, wherein the surfaces on both sides of the folded line are joined by a hinge at a finite distance.
[Feature 16]
By cutting a polygonal structure having an arbitrary polygon on the bottom surface on a plane perpendicular to the bottom surface, it is separated into quadrangular prisms with multiple openings, and the quadrangular prisms with each separated opening are featured in 2-6. It is characterized in that it is formed by selecting from the described quadrangular prisms having openings and joining the quadrangular prisms having the openings with hinges along the cutting line of the polygonal structure to form a mountain fold fold line. A polygonal prismatic structure that can be folded by rotation around ridges and folds without surface deformation.
[Feature 17]
By cutting a polygonal structure having an arbitrary polygon on the bottom surface on a plane perpendicular to the bottom surface, it is separated into quadrangular prisms with multiple openings, and the quadrangular prisms with each separated opening are featured in 8 to 15. It is characterized in that it is formed by selecting from the described quadrangular prisms having openings and joining the quadrangular prisms having the openings with hinges along the cutting line of the polygonal structure to form a mountain fold fold line. A polygonal prismatic structure that can be folded by rotation around ridges and folds without surface deformation.

10 Hollow square columnar structure 12 1st end wall 14 2nd end wall 16 1st side wall 18 2nd side wall 20 3rd side wall 22 4th side wall 50 Bottom surface 52 Square 54 Square 60 Bottom surface 62 Square 64 Square 66 Rectangle 70 Hollow square pillar structure 72 End wall 74 Side wall 76 Side wall 78 Side wall 80 Side wall 100 Hollow square pillar structure 102 End wall 104 End wall part 106 End wall part 108 Side wall 110 Side wall 112 End wall part 114 End wall part 116 Side wall Part 118 Side wall part 120 Side wall part 122 Side wall part

Claims (9)

Congruent quadrilateral V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2,1} (n = 1, 2) is the bottom surface, and the surface around the hinged line It is a hollow quadrangular columnar structure that can be folded without deformation of the surface by the rotation of, and the side surfaces V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i that can be folded together with the bottom surface. , 1} (i = 1, 2) is the "wall side", the side that moves with the deformation of the bottom without folding itself V _{1,1, j} V _{1,2, j} V _{2,2, j} A hollow quadrangular columnar structure characterized by having the following three configurations when V _{2,1, j} (j = 1, 2) is defined as a "cover side surface".
Configuration 1: Folding configuration in the boundary area between the bottom surface and the side surface of the wall.
Configuration 2: A configuration that eliminates surface interference due to folding along the folding line at the center of the bottom surface and the side surface of the wall.
Configuration 3: A configuration that eliminates surface interference due to folding in the boundary region between the lid side surface and the wall side surface. The hollow square columnar structure according to claim 1, wherein the configurations 1, 2 and 3 shown below are used.
Configuration 1: With _{respect to the vertices V n, i, j} constituting the bottom surface, an isometric bisector of the internal angle in the bottom surface is drawn from the _{vertices V n, i, j and the end points Q n, i, j, in the bottom surface. Set 0} . From Q _{n, i, j, 0} , let the foot of the perpendicular line drawn on _{the ridgeline V n, i, 1} V _{n, i, 2} of the boundary between the side surface and the bottom surface of the wall that is in close contact be the _{point Q n, i, j, 1.} , Line segment Q _{n, i, j, 0} Q _{n, i, j, 1} Two points from the closest point Q _{n, i, j, 0 on Q n, i, j, 2} , Q _{n, i, Take j, 3} . Line segment V _{n, i, j} Q _{n, i, j, 0} , Q _{1, i, j, 1} Q _{2, i, j, 1} is a valley fold line, line segment Q _{n, i, j, 0} Q _{n , i, j, 2} , V _{n, i, j} Q _{n, i, j, 1} is a mountain fold line, V _{n, i, j} Q _{n, i, j, 2} and V _{n, i, j} Q _{n, For i, j, 3} one is a mountain fold line and the other is a valley fold, and slits (linear cutting) are provided in _{Q n, i, j, 2} Q _{n, i, j, 1 (n).} = 1,2; i = 1,2; j = 1,2). Wall side V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} V _{2, i, 1} If lacking, vertices V _{1, i, 1} , V _{1, i, 2} , V _{2, i, It} is not necessary to provide this configuration for 2, V _{2, i, 1 (i = 1, 2).}
Configuration 2: Bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1} and adjacent wall side surface V _{1, i, 1} V _{1, i, 2} V _{2, i, 2} Let _{P n, i} be the intersection _{of the ridgeline of V 2, i, 1} and the folding axis AX _n (n = 1, 2, i = 1, 2). Two parallel line segments are provided on both sides of the line segment P _{n, 1} P _{n, 2 at} an equal distance t ₀ in the bottom surface, and the end point of the parallel line segment closest to the vertices V _{n, i, j is Z. Let n, i, j} , and the end point Z _{n, i, j} coincide with the point Q _{n, i, j, 0} (n = 1,2; i = 1,2,j = 1,2). Furthermore, the intersection of the line segment Q _{n, i, 1,0} Q _{n, i, 2,0} and the line segment P _{n, 1} P _{n, 2 is set to S n, i, 0} , and the intersection S _{n, i, 0 is the} latest. Let the foot of the perpendicular line drawn on _{the ridge line V n, i, 1} V _{n, i, 2} of the boundary between the side surface and the bottom surface of the wall in contact be the _{point S n, i, 1} (n = 1, 2; i = 1, 2). ). At this time, the line segments S _{n, i, 0} S _{n, i, 1} , Z _{n, 1, j} Z _{n, 2, j} are set as valley fold lines in the _{bottom surface, and the line segments Q n, i, 1, k} Q _{n , I, 2, k} are provided with slits (n = 1, 2, i = 1, 2, k = 0, 1), and the line segments S _{1, i, 1} S _{2, i, 1} are defined as mountain fold lines. (I = 1,2; j = 1,2). Wall side wall side _{V 1, i, 1 V 1} , i, 2 V 2, i, 2 V 2, i, 1 in the case where any one or constructed lacked both I was not provided endpoint Z _{n , i, j} are the intersections of the parallel lines and the ridges V _{n, i, 1} V _{n, i, 2.}
Configuration 3: A parallel line is provided in the side surface of the wall at a distance of t _{1 with respect to the ridge line V 1, i, j} V _{2, i, j at} the boundary between the side surface of the wall and the side surface of the lid, two points are taken on the line, and the apex is taken. Let the points close to _{V 1, i, j} , V _{2, i, j be R 1, ij} , R _{2, i, j} , respectively. Here, the line segment R _{1, ij} R _{2, ij is provided} with a valley fold line, and the line segments V _{1, i, j} R _{1, ij} , V _{2, i, j} R _{2, ij} are provided with slits. (I = 1,2; j = 1,2). Bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1 If} one or both are missing and configuration I is not provided, point R _{n, i and j} are the intersections of the parallel lines and the ridge lines V _{n, i, j} Q _{n, i, j, 1} and no slits are provided in the line segments V _{n, i, j} R _{n, i, j} (n =). 1,2; i = 1,2; j = 1,2). Bottom surface V _{n, 1,1} V _{n, 1,2} V _{n, 2,2} V _{n, 2, 1} thickness T _{n, b} (n = 1, 2), wall side surface V _{1, i, 1} V ₁ When the thickness of _{, i, 2} V _{2, i, 2} V _{2, i, 1 is T i, w} (i = 1, 2), the distances t ₀ and t ₁ satisfy the following conditions at the same time. The hollow square columnar structure according to claim 2.

Here, the distance between any point A and point B is represented by L (A, B), U ₁ = L (P _1,1,0 , P _1,1,1 ), U ₂ = L (P). _It is defined as 1,2,0, _P1,2,1). The hollow square columnar structure according to claim 3, wherein when determining points R _{n, i, j} (n = 1,2; i = 1,2; j = 1,2), the following conditions are satisfied. body.
Q _{n, i, j, 1} V _{n, i, j} R _{3-n, i, j} ＞ ∠ Q _{n, i, j, 1} V _{n, i, j} R _{n, i, j} ≧ α _{i, j} ( n = 1,2; i = 1,2; j = 1,2) Regarding the length of the polygonal line Q _{n, i, j, 0} Q _{n, i, j, k} (n = 1,2; i = 1,2; j = 1,2; k = 2,3), both of the following The hollow square columnar structure according to claim 4, wherein the condition is satisfied.
0 <g _{n, i, j, 3} <0.83
g _{n, i, j, 3} <g _{n, i, j, 3} <0.95
Here, g _{n, i, j, i} = L (Q _{n, i, j, 0} Q _{n, i, j, k} ) / L (Q _{n, i, j, 0} Q _{n, i, j, 1)} ) (N = 1,2; j = 1,2; k = 2,3). For a hollow polygonal columnar structure whose bottom surface is an arbitrary polygon with more sides than a quadrangle, it is divided into a hollow square columnar structure lacking a lid side surface corresponding to a cut surface at a dividing surface perpendicular to the bottom surface. Then, each of the divided hollow quadrangular columnar structures is made into the quadrangular columnar structure according to any one of claims 1 to 5, and the sides around the divided surface are joined as mountain fold lines. A characteristic foldable hollow polygonal columnar structure. The hollow square columnar according to claim 6, wherein the surface is cut once at all the polygonal lines, the ridges, and the slits, and the hinges are installed at the valley folds corresponding to the respective polygonal lines to join the cut surfaces. Structures and hollow polygonal columnar structures. The hollow square columnar structure and a hollow polygonal columnar structure according to claim 7, wherein the polygonal line is replaced with a flexible material having a finite width t'to join the replacement surfaces.
The width t of the flexible material 'is so T the thickness of the two surfaces to be joined respectively' _1, T _'2 to the time, the following conditions are satisfied.
_{T '1 + T' 2 <} t ' The hollow square columnar structure and a hollow polygonal columnar structure according to claim 8, wherein the flexible material is an FRP hinge.
Here, the FRP hinge forms a linearly continuous region in which the matrix resin does not substantially exist in the plate material made of the fiber reinforced resin composite material, and impregnates the plate material as it is or instead of the matrix resin with a flexible resin. It binds rigid fiber-reinforced composite materials.

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