JP2013230820A - Foldable three-dimensional structure and method of producing the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of producing a foldable three-dimensional structure which produces an enclosed three-dimensional shape such as a spherical shape, elliptical shape, or spheroid shape easy to fold flat from the three-dimensional shape, and to provide the three-dimensional structure.SOLUTION: A method of producing a foldable three-dimensional structure, includes: setting an axis penetrating a three-dimensional model; defining two axis points in the vicinity of points of intersection of the three-dimensional model and the axis; defining n intermediate points between the two axis points; defining a pair of top planes passing through the axis points, respectively; defining n first planes passing through n intermediate points, respectively, and perpendicular to the axis; defining m second planes sharing the axis and not parallel to each other; defining a plurality of top planar points at or about the points of intersection of the top planes, second planes, and the three-dimensional model; defining a plurality of planar points at or about the points of intersection of the first planes, second planes, and the three dimensional model; connecting the top planar points on one top plane are connected to the top planar points on the other top plane through the planar points; and deciding the structural model.

Description

  The present invention relates to a foldable three-dimensional structure and a method for producing the same.

  Containers that are flat before assembly but can be three-dimensionalized and stored by assembling can be folded before use and are compact and convenient without taking up unnecessary places. It is applied to various fields such as transporting beverages and containers for storing cakes using cardboard (for example, see Non-patent Document 1 below).

  In addition, a mechanism for instantly developing a three-dimensional image from a plane by opening a book is also popular as a so-called pop-out picture book (see, for example, Patent Document 1 below).

http: // www. ekouhou. net / disp-b, 3040392. html

Japanese Patent No. 3761777

  However, since the technique described in Non-Patent Document 1 requires a plurality of steps for assembly, there is a problem that it is not easy to return to a flat surface once assembled into a solid body. In general, there are almost simple shapes, and there is a problem that it is difficult to form a curved body such as a sphere, egg shape, or spheroid.

  The technique described in Patent Document 1 is easy to fold from a solid to a plane, but is merely a combination of planes, and can create a sealed solid such as a sphere, egg shape, or spheroid. There is a problem that it is difficult.

  Therefore, the present invention provides a method for manufacturing a foldable three-dimensional structure that can be easily folded from a three-dimensional object to a flat surface and can create a sealed three-dimensional structure such as a sphere, egg shape, or spheroid, and the three-dimensional structure thereof. The purpose is to provide goods.

  The manufacturing method of the collapsible three-dimensional structure which concerns on one viewpoint which solves the said subject is (A) setting the basic axis which penetrates a three-dimensional model, and (B) two axial points of the vicinity where a three-dimensional model and a basic axis cross. (C) n intermediate points between two axial points, (D) a pair of top planes passing through any of the two axial points, and (E) any of the n intermediate points And n first planes perpendicular to the base axis are defined, (F) m second planes each including the base axis and not parallel to each other are defined, and (G) the top plane, the second plane, and the three-dimensional model A plurality of top plane points that are intersections or their neighboring points are determined, and (H) a plurality of on-plane points that are intersection points or their neighboring points of the first plane, the second plane, and the three-dimensional model are defined, and (I) one top plane Each top plane point is connected to each other via the top plane point and the surface point on the other top plane to define the structural model. That.

  Moreover, the three-dimensional structure according to the second aspect for solving the above problem is a three-dimensional structure having a pair of top plane members and a band member attached to the pair of top plane members, Each is provided with an insertion portion to be inserted into another adjacent belt member, and is bent in the middle of the distance between the center of tension of the top plane member and the pair of top plane members passing through the belt member.

  The booklet which concerns on one viewpoint which solves the above-mentioned subject has a pair of top plane members and a belt member attached to a pair of top plane members, and each belt member has other belt members adjacent to each other. A three-dimensional structure, which is provided with an insertion portion to be inserted and is bent in the middle of the distance between the tension centers of the pair of top plane members passing through the top plane member and the band member, is sandwiched between two adjacent pages. At the same time, one of the above pull centers is connected from each of the two pages, and when the two pages are opened, the three-dimensional structure is expanded, and when the two pages are closed, the three-dimensional structure is folded. It is arranged like this.

  As described above, the present invention provides a method for producing a foldable three-dimensional structure that can be easily folded from a three-dimensional object to a flat surface and that can create a sealed three-dimensional object such as a sphere, egg shape, or spheroid, and its three-dimensional structure. Things can be provided.

It is a figure which shows the outline of the three-dimensional structure which concerns on embodiment. It is a figure which shows the outline of the strip | belt member of the three-dimensional structure which concerns on embodiment. It is a figure which shows the state which folded the three-dimensional structure which concerns on embodiment. It is a figure which shows another example of the top plane member of the three-dimensional structure which concerns on embodiment. It is a figure which shows the utilization state of the other example of the top plane member of the three-dimensional structure which concerns on embodiment. It is a photograph figure which shows one state of the prototype of the three-dimensional structure which concerns on embodiment. It is a photograph figure which shows one state of the prototype of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is an image figure of the step of the manufacturing method of the three-dimensional structure which concerns on embodiment. It is a figure which shows the outline of the other example of the strip | belt member of the three-dimensional structure which concerns on embodiment. It is a figure which shows the state which folded the other example of the three-dimensional structure which concerns on embodiment.

  Embodiments of the present invention will be described below with reference to the drawings. However, the present invention can be implemented in many different modes and is not limited to the embodiments shown below.

(Embodiment 1)
FIG. 1 is a diagram showing an outline of a three-dimensional structure (hereinafter referred to as “the present structure”) 1 according to the present embodiment, and FIG. 2 is a three-dimensional band member 3 (one piece) according to the present embodiment. FIG. 3 is a diagram illustrating a state in which the three-dimensional structured particle according to the present embodiment is folded (a diagram when viewed from the upper surface). As shown in the figure, the structure 1 is a three-dimensional structure having a pair of top plane members 2 and a plurality of band members 3 attached to the pair of top plane members 2. Each is provided with an insertion portion 31 to be inserted into another adjacent band member 3 and is bent at an intermediate M between the top plane member 2 and the distance between the tension centers of the pair of top plane members 2 via the band member 3. ing. Moreover, the knob member 21 is attached | subjected to the tension | pulling center of the top plane member 2 which concerns on this embodiment.

  In the present embodiment, the structure 1 can be widened or folded by pinching and pulling or pushing the knob member 21 attached to the top plane member 2 and moving the pair of top plane members 2 away or close.

  In the three-dimensional structure according to the present embodiment, the pair of top plane members 2 is a member having a plane (top plane) that is useful when expanding or folding the three-dimensional structure. When the distance is widened, the three-dimensional structure swells, and when close, the three-dimensional structure can be folded. In the present specification, the direction of the axis that is pushed to bring the pair of top plane members 2 closer to each other or the direction of the axis that is pulled to move away from each other is referred to as a “tension direction”. It is a substantially vertical direction. The structure of the top plane member 2 is not limited, and may be a circular shape, an elliptical shape, or the like, but is a polygon such as a triangle, a quadrangle, a pentagon, or a hexagon according to the number of the band members 3. It is preferable.

  Moreover, in the three-dimensional structure according to the present embodiment, the shape of the pair of top plane members 2 may be the same or different. For example, when the three-dimensional structure is symmetric in the upper and lower directions in the tensile direction, the same is preferable. For example, when the three-dimensional structure is asymmetric in the tensile direction, it is preferable to make them different. Note that the size of the top plane member 2 can be adjusted as appropriate, and is small when the vertex of the three-dimensional structure is preferably close to a sharp shape, and large when the vertex of the three-dimensional structure is nearly flat. It is preferable to do. Further, by enlarging at least one of the top plane members 2 and allowing the top member 2 to be divided into the inner member 22 and the peripheral member 23, for example, as shown in the examples of FIGS. It is also possible to arrange and store the objects in the three-dimensional structure. The internal member 22 and the peripheral member 23 have claw portions 221 and 231 that are combined, and can be attached and detached by combining them.

  Further, in the present embodiment, the material of the top plane member 2 is not particularly limited, but is preferably composed of a sheet of paper or plastic in order to be lightweight and easy to fold. This is also possible with other sheets.

  Here, a knob member 21 is formed at the center of tension of the top plane member 2 according to the present embodiment. Here, the “tensile center” is a point provided on the top plane member 2, and is particularly limited as long as it is at a position where a distance between the pair of top plane members 2 can be applied or a force to attach the top plane member 2 can be applied. Although it is not performed, it is preferable that the belt-shaped member 3 attached to the top plane member 2 is in a position where it can be efficiently expanded without bending. For example, in the case of a regular polygon, the center of gravity can be positioned. As long as it is at the center of the top plane member 2, it is preferable. In addition, each tension | tensile_strength center of a pair of top plane member 2 exists on one axis | shaft (tensile axis | shaft) parallel to a tension | pulling direction, respectively.

  In this embodiment, the knob member 21 is literally attached to the top plane member 2 in order to pinch a three-dimensional structure. As long as it can be pinched, the structure is not limited and may be a simple tag. Thereby, the user can pinch the three-dimensional structure easily. The material of the knob member 21 is not particularly limited, and the same material as that of the top plane member 2 can be adopted.

  In the present embodiment, the top plane member 2 is provided with a plurality of band members 3. In the present embodiment, the band member 3 is a member that forms the side surface of the three-dimensional structure, and the shape is literally a substantially band shape. Moreover, both ends of the belt member 3 according to the present embodiment are connected to the pair of top plane members 2 as described above, and are folded or spread according to the distance between the pair of top plane members 2. Here, “substantially belt-like” means a state extending in one direction with a predetermined width, but the end is not necessarily a straight line, and may be a wave curve (for example, 20 and 21) and the widths need not always be the same. Rather, it is preferable from the viewpoint of preventing an unnecessary gap from being generated on the side surface of the three-dimensional structure, that the side close to the top plane portion is thin and thick near the folding portion.

  In the present embodiment, the band member 3 is formed with a plurality of folds 32, and the band member 3 is bent or stretched according to the folds. The number of folds is not particularly limited as long as it is one, but a plurality of folds is preferable because a finer shape can be realized.

  Further, in the present embodiment, the band member 3 is provided with an insertion portion 31 to be inserted inside the three-dimensional structure of another adjacent band member, so that the positional relationship with the other adjacent band member can be maintained. it can. The structure of the insertion portion 31 is not limited. For example, the portion where the insertion portion 31 is provided and the portion where the insertion portion 31 is not provided are alternately formed for each portion divided by folds. Is also preferable.

  In addition, the three-dimensional structure in the present embodiment has a crease at the midpoint of the distance between the tension centers of the pair of top plane members 2 passing through the top plane member 2 and the band member 3. It is bent at the eyes. By doing in this way, when folding a three-dimensional structure, the distance to an intermediate point and each tension | tensile_strength center can be made the same, and the bending of a strip | belt member and a top plane member can be prevented. That is, the intermediate point is a point at which the distance between the fold and each of the two tension centers becomes equal when the three-dimensional structure is folded into a plane.

  With the above configuration, the three-dimensional structure in the present embodiment can be folded or expanded. More specifically, the user can fold the three-dimensional structure by pinching the three-dimensional structure by pinching the pair of knob members 21 and pressing them in the direction of attaching the top plane member 2 and pulling in the opening direction.

  As described above, with the three-dimensional structure according to the present embodiment, a foldable three-dimensional structure that can be easily folded from a three-dimensional object to a plane and that can create a sealed three-dimensional object such as a sphere, egg shape, or spheroid Become. The three-dimensional structure according to the present embodiment can be applied as, for example, a booklet such as a picture book in which the three-dimensional structure spreads when opened or a storage box such as a cake. 6 and 7 are photographic diagrams of prototypes when an example is actually made as an example when a three-dimensional structure is used as a booklet such as a picture book. 6 shows an example when the booklet is closed, and FIG. 7 shows an example when the booklet is opened.

  Here, a method for producing the above foldable three-dimensional structure (hereinafter referred to as “the present method”) will be described. In this method, (A) a base axis penetrating the three-dimensional model is set, (B) two axial points in the vicinity where the three-dimensional model and the basic axis intersect are determined, and (C) n pieces of n-axis points between the two axial points. Define an intermediate point, (D) define a pair of top planes passing through any of the two axial points, and (E) define n first planes that pass through any of the n intermediate points and are perpendicular to the base axis (F) m second planes each including a base axis and not parallel to each other are defined, and (G) a plurality of top plane points that are intersections of the top plane, the second plane, and the three-dimensional model or their neighboring points are defined (H ) A plurality of on-surface points that are the intersections of the first plane, the second plane, and the solid model or their neighboring points are determined. (I) Each top plane point on one top plane is defined on each other on the other top plane. Connect the top plane point and the point on the surface, and (J) divide the structural model into two with any one of the n first planes as the boundary. The structural model respectively developed into a plane, define the structural model.

  This method can be performed by various methods. As a preferred method, a so-called computer is used, a program for executing the method is stored in a computer recording medium, and the program is executed. is there. That is, (A) a basic axis that penetrates the three-dimensional model is set in the computer, (B) two axial points in the vicinity where the three-dimensional model and the basic axis intersect are determined, and (C) n points between the two axial points. (D) a pair of apex planes passing through any of the two axial points, and (E) n first planes passing through any of the n intermediate points and perpendicular to the base axis (F) m number of second planes each including a base axis and not parallel to each other, (G) a plurality of top plane points that are intersections of the top plane, the second plane, and the three-dimensional model or their neighboring points, H) A plurality of on-surface points that are the intersections of the first plane, the second plane, and the three-dimensional model or their neighboring points are determined. (I) Each top plane point on one top plane is defined on each other top plane. A tie structure model is defined via the top plane point and the surface point of (J), and (J) one of the n first planes as a boundary. Dividing the structural model into two, respectively deployed in a plane two structural model may be a program for the production of collapsible three-dimensional structure.

  First, the method includes the step of (A) setting a base axis A2 that penetrates the three-dimensional model A1. Here, the “three-dimensional model” refers to a model of an actual three-dimensional shape that is the basis of a three-dimensional structure. The three-dimensional shape may be a curved surface or may be formed simply by a combination of planes, and the shape is not limited. When this step is realized by a computer program, it is preferable to use detailed three-dimensional coordinate data of the three-dimensional model.

  In this step, first, one base axis A2 that penetrates the three-dimensional model A1 is set. The method of selecting the base axis A2 is not particularly limited as long as it can penetrate the three-dimensional model and the three-dimensional structure can be manufactured, but it is preferable to set an axis with the highest symmetry. An image diagram in this case is shown in FIG. 8, for example. In addition, this figure is an image figure of the longitudinal cross-section of a three-dimensional structure.

  The method further includes (B) determining two axial points in the vicinity where the three-dimensional model A1 and the base axis A2 intersect. By defining the basic axis A2, two intersections B1 where the three-dimensional model A1 and the basic axis A2 intersect can be obtained. Based on this, each point in the vicinity of the intersection B1 is set as an axis point B2.

  The axis B2 may be the intersection B1 itself, but the three-dimensional structure according to the present embodiment has a top plane. In order to obtain various points based on the intersection of the top plane and the three-dimensional model, Although it is not necessarily limited, from the viewpoint of bringing the three-dimensional structure closer to the shape of the three-dimensional model, it is arranged inside the three-dimensional model A1 from the intersection B1, more specifically, inside the pair of intersections B1. preferable. An image diagram in this case is shown in FIG. In addition, this figure is an image figure of the longitudinal cross-section of a three-dimensional structure.

  Further, the method includes a step (C) of defining n intermediate points C1 to Cn between two axial points. The n distances may be arranged at equal intervals, but may be different. If they are equal, there is an advantage that calculation required for manufacturing becomes easy. By making them different, the shape of the three-dimensional model A1 can be made closer to the shape of the three-dimensional model A1 when the shape of the three-dimensional model A1 is complicated. There is an advantage of becoming. Here, n is not particularly limited as long as it is 1 or more. However, from the viewpoint of facilitating bending, it is preferably 2 or more, and an odd number is preferable because the midpoint becomes clearer. FIG. 10 shows an image diagram in this case (an example in which n is 5). In addition, this figure is an image figure of the longitudinal cross-section of a three-dimensional structure.

  The method also includes (D) a step of defining a pair of top planes D1 and D2 that pass through one of the two axial points. Since the top plane is determined for each of the two upper and lower axial points, two parallel top planes are formed. This top plane is the same surface as the top plane of the three-dimensional structure. An image diagram of the planar arrangement in this case is shown in FIGS. FIG. 11 is a perspective image view, and FIG. 12 is a longitudinal cross-sectional image view.

  The method further includes (E) defining n first planes E1 to En passing through any of the n intermediate points and perpendicular to the base axis A2. As a result of the above (D) and (E), n + 2 planes perpendicular to the base axis A2 and arranged in parallel to each other are formed. An image diagram in this case is shown in FIGS. This figure is a perspective view. FIG. 13 is a perspective image diagram, and FIG. 14 is a longitudinal cross-sectional image diagram.

  In the method, the method further includes (F) defining m second planes each including the base axis A2 and not parallel to each other. An image diagram in this case is shown in FIGS. These drawings show an example in which m is six, FIG. 15 is a perspective image diagram, and FIG. 16 is an image diagram of the second plane F1 to Fm when viewed from the axial direction of the base axis A2. As shown in these drawings, the plurality of second planes are arranged radially around the base axis A2. Of the m second planes, the angles formed by the close planes may be uniform or non-uniform. If it is uniform, the three-dimensional structure can be easily manufactured and the force applied to the three-dimensional structure can be made uniform in the direction around the base axis. Even if it exists, there exists an advantage that it can match | combine well with this shape and reproducibility becomes high.

  The method also includes (G) a step of determining a plurality of top plane points G1 and G2 that are intersections of the top plane, the second plane, and the three-dimensional model or their neighboring points. By this step, the shape of the top plane member can be determined, and the shape of the top plane member is a polygon having 2m vertices. In this case, it is preferable that the top plane points G1 and G2 are intersections of the three-dimensional model itself. However, for adjustment in determining the intermediate point described later, or the three-dimensional model is a set of a plurality of three-dimensional coordinate data. In the case where the three-dimensional coordinate data does not exist on a straight line formed by the intersection of the top plane and the second plane, the position points in the vicinity may be used as the top surface points G1 and G2. An image of the top plane point G1 in this case is shown in FIGS. FIG. 17 is an image diagram of a longitudinal sectional view, and FIG. 18 is an image of a top plane member obtained as a result of the above. The top plane member has a shape in which a plurality of top plane points G1 (G1a to G1l in the example of FIG. 18) on the same plane are connected by lines.

  Further, in this method, as in (G) above, the method includes (H) determining a plurality of on-plane points H1 to Hn that are intersections of the first plane, the second plane, and the three-dimensional model or their neighboring points. By this step, the point on the side surface of the three-dimensional structure, more specifically, the position of the fold can be determined. In this case, it is preferable that the on-surface point H1 is the intersection of the stereo model itself. However, for adjustment when determining the intermediate point, or the stereo model is a set of a plurality of three-dimensional coordinate data, and In the case where the three-dimensional coordinate data does not exist on a straight line formed by the intersection of the first plane and the second plane, the position point in the vicinity may be used as the top surface point H1. An image diagram in this case is shown in FIG.

  In this method, (I) each top plane point on one top plane is connected to each top plane point on the other top plane via a surface point. Thereby, the boundary line of each belt member can be clarified, and a belt member can be formed. In this case, it is convenient and preferable to connect the points with straight lines, but the points may be connected with curves. If it is set as a curve, the area which the adjacent belt members overlap can be increased, and there exists an advantage that a three-dimensional shape can be folded and assembled more stably. In addition, the image figure of the strip | belt member (one half) at the time of connecting with this curve is shown in FIG. 20, and the schematic of the top plane member in which this strip | belt member was connected in multiple numbers is shown in FIG. 2 is the same as that of FIG. 2, but only half of the band member of FIG. 20 is shown, and actually the same members are vertically joined.

  The method preferably further comprises (J) a step of dividing the structural model into two with any one of the n first planes as a boundary, and developing the two structural models on each plane. In this way, the structural model can be developed on a plane such as paper, and the structural model developed on this plane can be cut out and assembled into half solid structures. By combining these three-dimensional structures, a three-dimensional structure that can be folded is obtained. In this case, it is preferable that the boundary to be divided into two is an intermediate point of the distance between the two top plane points and the two axial points passing through the on-plane points. By doing in this way, when a three-dimensional structure is folded, it can prevent that a bending etc. will arise. In this step, it is also preferable to add a process for forming an insertion portion in a region divided by the folds of the band members that are developed and formed.

  Further, in this method, (H) a step of determining a plurality of surface points that are intersections of the first plane, the second plane, and the three-dimensional model or their neighboring points, and (I) each top plane point on one top plane Are connected to each top plane point on the other top plane via an on-plane point, and (K) either one of the top plane point G1 or the on-plane point H1 is moved, and It is also preferable to include a step of connecting each top plane point on one top plane to each top plane point on the other top plane via a surface point. By doing in this way, when each point is obtained by the steps of (H) and (I) above, when the intermediate point cannot be determined well in (J), the on-surface point can be determined again. A more stable three-dimensional structure can be manufactured.

  Further, in the above process, it is preferable to provide a step of setting the half point of the distance between the center of tension, that is, the two axial points B2, via the top plane point and the plurality of surface points as an intermediate point. In determining this, the step of moving the top plane point or the on-plane point may be performed together. By doing in this way, an intermediate point can be determined reliably.

  In the present embodiment, the above-described steps (A) to (J) have been described step by step. However, steps other than the steps in the dependency relationship may be performed simultaneously, and the order of steps may be changed.

  As described above, according to the present embodiment, a method for manufacturing a foldable three-dimensional structure that can be easily folded from a three-dimensional object to a flat surface and can create a sealed three-dimensional object such as a sphere, egg shape, or spheroid, and the three-dimensional structure thereof Things can be provided.

  The present invention has industrial applicability as a three-dimensional structure and a manufacturing method thereof.

Claims (7)

Set the base axis that penetrates the 3D model,
Two axial points in the vicinity where the solid model and the base axis intersect are defined,
N intermediate points are defined between the two axis points;
A pair of top planes passing through either of the two axial points are defined;
N first planes passing through any of the n intermediate points and perpendicular to the base axis are defined;
Defining m second planes each including the base axis and not parallel to each other;
Determining a plurality of top plane points that are intersection points of the top plane, the second plane, and the solid model or their neighboring points;
A plurality of on-surface points that are intersections of the first plane, the second plane, and the solid model or their neighboring points are determined,
A method for producing a collapsible three-dimensional structure, wherein each top plane point on the one top plane is connected to each top plane point on the other top plane via the on-plane point to define a structural model. Dividing the structural model into two with any one of the n first planes as a boundary;
The method for manufacturing a three-dimensional structure according to claim 1, wherein the two structural models are each developed on a plane.   The method for manufacturing a three-dimensional structure according to claim 2, wherein an intermediate point of a distance between the two axis points passing through the pair of top plane points and the surface point is the boundary.   The manufacturing method of the three-dimensional structure of Claim 1 which divides | segments the said structural model so that it may have a some strip | belt part along said 2nd plane, and expand | deploys to a plane. A pair of top plane members;
A band member attached to the pair of top plane members,
Each of the band members is provided with an insertion portion to be inserted into another adjacent band member,
A three-dimensional structure that is bent in the middle of a distance between tensile centers of a pair of top plane members that pass through the top plane member and the band member.   The three-dimensional structure according to claim 5, wherein a knob member is attached to the tension center. A pair of top plane members and band members attached to the pair of top plane members, and each of the band members is provided with an insertion portion to be inserted into another adjacent band member, A three-dimensional structure bent in the middle of the distance between the tensile centers of the pair of top plane members passing through the member and the band member is sandwiched between two adjacent pages, and the pulling is performed from each of the two pages. A booklet that is arranged so that the three-dimensional structure is expanded when the two pages are opened with the center connected, and the three-dimensional structure is folded when the two pages are closed. .