JP3225115B2 - 32-hedron globe material and method of making the same - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for manufacturing a globe by cutting out thick paper to form a polyhedron and printing a map on the thick paper in advance. However, in the present invention, the term "cardboard" includes a sheet for cardboard made of a synthetic resin, and the term "cutout" includes the meaning of "pulling out" or "peeling off".

[0002]

2. Description of the Related Art It is publicly known that a globe is formed by cutting out thick paper and assembling a polyhedron. FIG. 6B is a perspective view of a known dodecahedral globe. Such a conventional icosahedral globe is developed on cardboard, is provided with glue margins or insertion pieces to make intermittent cuts in the contours, and indents along the fold lines. And printed as a globe material with a map printed on 12 regular pentagons spread on the cardboard. The globe material thus constructed is in the form of a thin plate, which is convenient for transportation and storage, suitable as a teaching material for children and a hobby for adults, and also includes a piggy bank, a toy, a desk accessory, and an advertisement. There are various uses such as use.

[0003]

The dodecahedral cardboard globe shown in FIG. 6 (B) is not sufficiently similar to a perfect sphere. For example, the equator 1 shown by a chain line is not circular. ,
It is unnatural because it does not match the ridge. There are five types of regular polyhedrons, and their external shapes are as shown in FIG. FIG.
A is a regular tetrahedron, B is a regular hexahedron, C is a regular octahedron,
D is a regular dodecahedron, and E is a regular icosahedron. A Examples of these development view than as shown in FIGS 8, a positive 4
B is a development view of a regular hexahedron, c is a development view of a regular octahedron, d is a development view of a regular dodecahedron, and e is a development view of a regular icosahedron. In order to obtain a feeling similar to a sphere, it is inappropriate if the number of faces is smaller than the above-mentioned regular dodecahedron, and it is desirable that the number of faces is greater. The polyhedron is only a regular icosahedron. However, positive 2
In the case of the octahedron, the feeling close to a sphere is still insufficient, and the sharp impression of the twelve vertices is intense.

What can be considered is the use of a composite polyhedron composed of two types of regular polygons. For example, in a soccer ball, as shown in the developed view of FIG. 9, a 32-hedron composed of 12 equal pentagons and 20 regular hexagons having the same side length as the regular pentagon is formed. It's being used. By cutting the leather into such a shape and stitching it (including the seam allowance), as shown in FIG. However, if the cardboard is cut out according to the development shown in FIG. 9 to form a 32-hedron globe, the following problem occurs. That is, FIG. 10B is an enlarged view of a portion J surrounded by a chain line in FIG. The apex angle of a regular hexagon is 120
Since the vertex angle of the regular pentagon is 108 degrees, the angle θ of the illustrated valley-shaped cut portion K is 12 degrees. Since this angle θ is very small (12 degrees), it is extremely difficult to provide a margin for glue or an insert in this portion. It is almost impossible to assemble this even if the glue allowance or the insert is forcibly provided. The present invention has been made in view of the above circumstances, and has as its object to provide a technology that can be assembled without special skill, and that forms a globe close to a sphere by cardboard. .

[0005]

The basic principle of the present invention created to achieve the above object will be described below with reference to FIGS. 1 and 6A corresponding to the embodiment. It is. That is, when a hexahedron having the appearance as shown in FIG. 6A is developed on cardboard, it becomes 12 regular pentagons and 20 regular triangles as shown in FIG. When this developed figure is cut out with an appropriate insert or glue margin attached and assembled as shown in FIG. 6A, a polyhedron having a feel close to a sphere is obtained. If a map is printed in advance on the developed figure in FIG. 1, a globe having a feeling close to a sphere is formed.

[0006]

The 32-hedron (soccer ball) shown in FIG. 10A as a conventional example is an expanded view of FIG. 10B.
The cut angle of the valley K in FIG. 2A, which is a partially enlarged view of FIG. 1, is 24 degrees as compared with the cut angle of the valley K in FIG. For this reason, it is possible to form the insertion piece and the glue allowance, and the assembling work is also easy. Further, in the 32-hedron shown in FIG. 6A, when an arbitrary regular pentagon is placed on a desk as a bottom surface, a cut 1 ′ (indicated by a chain line) formed by a horizontal plane that divides this vertically into two halves coincides with a ridge line. If the map is printed so that these ridges are set to the equator, a globe having a natural feeling without giving a strange feeling can be obtained.

[0007]

FIG. 1 shows an example of a developed figure of a hexahedral globe according to the present invention.
Pentagons and eight regular triangles T1 to T8
And square, and a twelve equilateral triangle T0 becomes more and (T0 marked with suffixes _1, T0 ₂ and T0 ₉ ~T0 ₁₁ a included) total 32 regular polygon. (All pentagons in the present invention are regular pentagons, so they may be simply referred to as pentagons, and similarly, regular triangles may be abbreviated as triangles.)

The pentagon and the triangle have the same side length. In addition, 8 triangles T1 to T8 and 12 triangles T0
Are triangular with each other, but T1 to T8 are constrained by connecting two or more of the three sides to a pentagon, and T0 is connected by connecting only one side to a pentagon. There is only. Of the 12 triangles T0, T0 ₉ ～T0 ₁₁ triangular T0 to receive but other nine constraints are less expansion techniques restraint. This will be described later in detail.

FIG. 2 is an explanatory diagram of the cutting angle φ of the valley K formed between the triangle T5 and the pentagon P2. Since the apex angle of the regular pentagon is 108 degrees and the apex angle of the regular triangle is 60 degrees, the cutting angle φ is 24 degrees. This value is twice as large as the cutting angle θ of 12 degrees in the conventional example shown in FIG. 10B. Using this large cutting angle, (A)
It is easy to provide the insertion piece 2 and the insertion hole 3 as shown in the figure, and it is also easy to provide the glue allowance 4 as shown in FIG. In practicing the present invention, an insertion piece / insertion hole or glue allowance (both not shown) is attached to the outline of the solid line shown in FIG. 1 on cardboard, and an intermittent cut is made with a fingertip. In addition to cutting through, a linear indentation is provided along a fold line shown by a broken line in FIG.

[0010] In order to industrially produce and economically supply the globe material constituted as described above, there is a problem how to develop the 32-hedron. Now, if 12 regular pentagons and 20 regular triangles (however, the regular pentagons and the side lengths are equalized) are cut out from cardboard, and these are arranged on a desk, an extremely large number of arrangements are required. Yes. In other words, there are many methods of developing the 32-hedron shown in FIG. However, as a practical problem, it is desired that the developed figure fits in a rectangular sheet (the ratio of the long side to the short side is about 1.4 times). In other words, given the length of one side (length of the ridge) representing the size of the 32-hedron, expansion into a rectangle with a minimum area (ratio 1.4) is performed.
If the rectangular dimensions of the paper are specified, for example, as A5 or B5, it is desirable to expand the largest hexahedron into it.

FIG. 1 shows one of the recommended development examples. Considering this, the twelve regular triangles denoted by the symbol T0 (including those with a suffix) have only one side thereof. It is connected to one side of a regular pentagon and has few restrictions on the expansion technique. That is, regular triangle T0 ₁ which is connected with the positive pentagon P4 is can be moved to the position of t ₁ showing it in chain line, likewise regular triangle T0 ₂ is transferred to t ₂ position be able to.

With the above degrees of freedom taken into consideration, the expansion method shown in FIG. 1 is specified in FIG. 3 except for the nine regular triangles T0 shown in FIG. But Figure 1
It is a diaphysis part which specifies the example of deployment of.

FIG. 5 is a view for explaining the above-mentioned developing method.
As shown in (A), an arbitrary side of the regular pentagon is named base a, the left side adjacent thereto is named side b, and the right side is similarly named side c. A side connecting the vertex and the side b is named a side d, and a side connecting the vertex and the side e is a side e.
Name it. An arbitrary side of the regular triangle shown in FIG. 5B is named base f, a left oblique side is named side g, and a right oblique side is named side h. Then, as shown in FIG. 3, a first triangle T1 is arranged substantially at the center of the cardboard, a base a is overlapped with a side g of the first triangle T1, and a first pentagon P1 is arranged. The base f is overlapped with the side e of the first pentagon P1 to form a second
A second pentagon P2 is disposed by arranging a polygon T2, overlapping an arbitrary side on a side h of the second triangle T2, and arranging a base a on a side g of the triangle T2. A third pentagon P3 is arranged, a base f is overlapped on a side b of the third pentagon P3, a third triangle T3 is arranged, and an arbitrary side is arranged on a side h of the third triangle T3. Are superimposed to arrange a fourth pentagon P4, and the base f is set on the side d of the third pentagon P3.
Are overlapped with each other to arrange the fourth triangle T4, and any side is overlapped with the side h of the fourth triangle T4 to form the sixth triangle T4.
Is arranged, and the base f is overlapped with the side c of the third pentagon P3 to arrange the fifth triangle T5, and an arbitrary side is set to the side g of the fifth triangle T5. Are superimposed to arrange a fifth pentagon P5, and the first triangle T1
A seventh pentagon P7 is arranged by superimposing the base a on the side h, and a sixth triangle T6 is arranged by superimposing the base f on the side e of the seventh pentagon P7. An eighth pentagon P8 is arranged by superimposing the base a on the side h of the sixth triangle T6, and by superimposing an arbitrary side on the side g of the sixth triangle T6 to form a ninth pentagon P9. And the eighth
The seventh triangle T7 is arranged by superimposing the base f on the side e of the pentagon P8, and the tenth pentagon P10 is arranged by superimposing an arbitrary side on the side h of the seventh triangle T7. At the same time, the eleventh pentagon P11 is arranged by superimposing the base a on the side g of the seventh triangle T7,
An eighth triangle T8 is arranged by superimposing a base f on one side b, and a twelfth pentagon P12 is arranged by superimposing an arbitrary side on a side h of the eighth triangle T8; further, with arranging the triangle T0 ₉ ninth by superposing arbitrary edge to edge e of the third pentagon P _3, 5 of the 8
Place the triangle T0 ₁₀ of the 10 by superimposing any side to side c of the square P8, and triangle T0 ₁₁ of the 11 by superimposing any side to side c of the first pentagonal P1 Place.

As can be easily understood from FIG. 1, even if a graphic which is a line object to this developed graphic (that is, a graphic obtained by turning over this FIG. 1) is used, as in the above embodiment, The 32-hedron can be conveniently spread on rectangular cardboard. FIG. 4 is an exploded view of an embodiment different from that of FIG. 3, and the designation of each side of the pentagon and the triangle is the same as the designation of the embodiment shown in FIG. As in the embodiment of FIG. 3, a first triangle T1 is arranged substantially at the center of the cardboard,
The first triangle T1 is overlapped with the base a on the side g to form a first triangle T1.
Is arranged, a base f is overlapped with a side e of the first pentagon P1, and a second triangle T2 is arranged.
Any side is superimposed on the side h of the triangle T2 of
In addition to arranging the polygon P2, the third pentagon P3 is arranged by superimposing the base a on the side g of the triangle T2.
The third triangle T3 is arranged by overlapping the base f on the side b of the pentagon P3, and the fourth pentagon P4 is arranged by overlapping an arbitrary side on the side h of the third triangle T3. Then, the base f is overlapped with the side d of the third pentagon P3 to arrange the fourth triangle T4, and an arbitrary side is overlapped with the side h of the fourth triangle T4 to form a sixth triangle. A pentagon P6 is arranged, a base f is overlapped with a side c of the third pentagon P3 to arrange a fifth triangle T5, and an arbitrary side is arranged on a side g of the fifth triangle T5. A fifth pentagon P5 is arranged by superimposition, a base a is superimposed on a base f of the first triangle T1, a seventh pentagon P7 is arranged, and the seventh pentagon P7 is arranged.
The sixth triangle T is formed by superimposing the base f on the side d of the polygon P7.
6 is arranged, the base a is overlapped with the side g of the sixth triangle T6, and the eighth pentagon P8 is arranged.
An arbitrary side is superimposed on the side h of the triangle T6 of
A polygon P9 is arranged, a base f is overlapped with the side d of the eighth pentagon P8, a seventh triangle T7 is arranged, and an arbitrary side is overlapped with the side g of the seventh triangle T7. Tenth
While arranging the polygon P10, the eleventh pentagon P11 is arranged by overlapping the base a with the side h of the seventh triangle T7, and the base f is overlapped with the side c of the eleventh pentagon P11. The eighth triangle T8 is arranged in the same manner as described above, and an arbitrary side is superimposed on the side g of the eighth triangle T8 to form a twelfth triangle T8.
Place a square P12, further with placing the triangle T0 ₉ ninth by superposing arbitrary edge to edge e of the third pentagon P _3, optionally the sides b of the pentagon P8 eighth Are overlapped with each other to arrange a _tenth triangle T010.

The same effect can be obtained by expanding the developed view of the embodiment shown in FIG. 4 so that the figure is turned upside down.

[0016]

As described above, the use of the globe material of the present invention makes it possible to easily assemble a cardboard globe consisting of a 32-hedron having a feeling close to a sphere without special skill. Can be. Further, according to the method for producing a globe material of the present invention, the globe material according to the present invention can be economically produced.

[Brief description of the drawings]

FIG. 1 is a plan view showing an embodiment of a material for a 32-hedron globe according to the present invention, from which inserts or glue allowance are removed.

FIG. 2 is shown to explain the operation and effect of the embodiment. It is a top view near a triangle T5.

FIG. 3 is an exploded view of a diaphysis of an embodiment of the method for producing a material for a 32-hedron globe according to the present invention.

FIG. 4 is an exploded view of a diaphyseal part, showing an embodiment different from the above-described embodiment, in which the arrangement of the same components is different.

5 (A) is an explanatory view of the reference numerals attached to the regular pentagon in FIGS. 3 and 4, and FIG. 5 (B) is an explanatory view of the reference numerals attached to the same triangle.

FIG. 6A is a perspective view of a 32-hedron applied to the present invention,
(B) is a perspective view of a conventional globe.

FIGS. 7A, 7B, 7C, and 7E are perspective views of five types of regular polyhedrons that can exist.

FIGS. 8A, 8B, 8C, and 8D are examples of developments of the above five types of regular polyhedrons.

FIG. 9 is an example of a development view for forming a known 32-hedron used for a soccer ball.

FIG. 10 (A) is a perspective view of the above-mentioned 32-hedron, and FIG. 10 (B) is an explanatory view of a problem in the above developed view.

[Explanation of symbols]

1,1 '... Equator drawn on a polyhedral globe, 2, ...
Insertion piece, 3 ... insertion hole, 4 ... glue allowance.

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-50-112131 (JP, A) JP-A-60-120473 (JP, U) (58) Fields investigated (Int. Cl. ⁷ , DB name) G09B 27/00-29/10

Claims (7)

(57) [Claims] 1. A hexahedron composed of 12 regular pentagons and 20 regular triangles having the same side length as the regular pentagon is developed on a cardboard, and the developed figure is assembled to form a hexahedron. Is formed, a flat map is printed on the developed figure of the cardboard so as to form a globe-like three-dimensional figure on the surface of the above-mentioned 32 face, and a margin for joining is added to the outline of the developed figure. 32. A globe material having a hexahedron, characterized in that it is provided with intermittent cuts and linear indentations are formed along the fold lines of the developed figure. 2. The joint blank portion is a pair of a plug-in piece and a projecting piece provided with a plug-in hole for each of 29 pairs of joint sides. The material for a globe of 32 faces according to claim 1. 3. The method according to claim 2, wherein the joining margin is a margin for glue. The material for a globe of 32 faces according to claim 1. 4. When a hexahedron composed of 12 regular pentagons and 20 regular triangles is developed on cardboard to constitute a material for a hexahedral globe, any one of the regular pentagons is used. The side is named base a, the left side adjacent to the base is named side b, the right side is named side c, the side connecting the above-mentioned side b and the vertex is side d, and the side c and the vertex are also named A side connecting the two sides is named side e, an arbitrary side of the regular triangle is named base f, a side adjacent to the left side of the base f is side g, and a side adjacent to the right side is also named side h. A first triangle T1 is arranged substantially at the center of the cardboard, and a base a is overlapped with a side g of the first triangle T1 to form a first triangle T1.
The first pentagon P1 has a base f overlapped with a side e of the first pentagon P1 to form a second pentagon P1.
Is arranged, an arbitrary side is superimposed on a side h of the second triangle T2, a second pentagon P2 is arranged, and a base a is superimposed on a side g of the triangle T2. A third pentagon P3 is arranged in such a manner that a base f is overlapped with a side b of the third pentagon P3 to form a third pentagon P3.
Is arranged, and a fourth pentagon P4 is arranged by superimposing an arbitrary side on a side h of the third triangle T3, and a base f is arranged on a side d of the third pentagon P3. A fourth triangle T4 is disposed by being overlapped with the fourth triangle T4.
A sixth pentagon P6 is arranged by superimposing an arbitrary side on the side h, and a fifth triangle T5 is arranged by superimposing a base f on the side c of the third pentagon P3. Fifth triangle T
A fifth pentagon P5 is arranged by superimposing an arbitrary side on the side g of 5, and a seventh pentagon P7 is arranged by superimposing a base a on the side h of the first triangle T1, The seventh pentagon P
The sixth triangle T6 is arranged by superimposing the base f on the side e of 7 and the base a by superimposing the base a on the side h of the sixth triangle T6.
And the sixth triangle T6
The ninth pentagon P9 is arranged by superimposing an arbitrary side on the side g, and the seventh triangle T7 is arranged by superimposing the base f on the side e of the eighth pentagon P8. The tenth pentagon P10 is arranged by superimposing an arbitrary side on the side h of the seventh triangle T7, and the base a is superimposed on the side g of the seventh triangle T7.
11 and the base f is superimposed on the side b of the eleventh pentagon P11 to arrange the eighth triangle T8, and an arbitrary side is superimposed on the side h of the eighth triangle T8. And the twelfth pentagon P
12 arranged, further, with arranging the triangle T0 ₉ ninth by superposing arbitrary edge to edge e of the third pentagon P _3, 8
5 triangular T0 ₁₀ of the 10 are arranged by overlapping any edge to edge c of the square P8, and side c of the first pentagonal P1 of
A method for manufacturing a material for a hexahedron globe, comprising arranging an _eleventh triangle T011 by superposing arbitrary sides on the globe. 5. A developed graphic obtained by inverting the developed graphic composed of the first to twelfth pentagons and the first to eleventh triangles arranged as described above. 3. The method for producing a 32-hedral globe material described in 1. above. 6. When a hexahedron consisting of 12 pentagons and 20 triangles is developed on cardboard to constitute a material for a 32-hedron globe, any one side of the pentagon is a base. a, the left side adjacent to the base is named side b, the right side is named side c, the side connecting the above-mentioned side b and the vertex is side d, and the side c is also named
A side connecting the vertex to the vertex is named side e. An arbitrary side of the triangle is named base f, a side adjacent to the left side of the base f is side g, and a side adjacent to the right side is side h. The first triangle T1 is arranged at substantially the center of the cardboard, and the base a is overlapped with the side g of the first triangle T1 to form the first triangle T1.
The first pentagon P1 has a base f overlapped with a side e of the first pentagon P1 to form a second pentagon P1.
Is arranged, an arbitrary side is superimposed on a side h of the second triangle T2, a second pentagon P2 is arranged, and a base a is superimposed on a side g of the triangle T2. A third pentagon P3 is arranged in such a manner that a base f is overlapped with a side b of the third pentagon P3 to form a third pentagon P3.
Is arranged, and a fourth pentagon P4 is arranged by superimposing an arbitrary side on a side h of the third triangle T3, and a base f is arranged on a side d of the third pentagon P3. A fourth triangle T4 is disposed by being overlapped with the fourth triangle T4.
A sixth pentagon P6 is arranged by superimposing an arbitrary side on the side h, and a fifth triangle T5 is arranged by superimposing a base f on the side c of the third pentagon P3. Fifth triangle T
Arrangement of a fifth pentagon P5 by superimposing an arbitrary side on the side g of 5 and arrangement of a seventh pentagon P7 by superimposing a base a on the bottom f of the first triangle T1; The sixth triangle T6 is arranged by superimposing the base f on the side d of the seventh pentagon P7, and the base a is superimposed on the side g of the sixth triangle P6 by the eighth.
And the sixth triangle T6
Arrange a ninth pentagon P9 by overlapping an arbitrary side on the side h, and place a seventh triangle T7 by overlapping a base f on the side d of the eighth pentagon P8. The tenth pentagon P10 is disposed by overlapping an arbitrary side on the side g of the seventh triangle T7, and the base a is superimposed on the side h of the seventh triangle T7.
11 and the base f is superimposed on the side c of the eleventh pentagon P11 to arrange the eighth triangle T8, and an arbitrary side is superimposed on the side g of the eighth triangle T8. And the twelfth pentagon P
12 arranged, further, with arranging the triangle T0 ₉ ninth by superposing arbitrary edge to edge e of the third pentagon P _3, 8
5 superimposed any side to side b of the rectangular P8, characterized in that the triangle T0 ₁₀ of the 10 arranged, 32 facepiece fabrication methods globes for materials. 7. A developed figure obtained by inverting a developed figure composed of the first to twelfth pentagons and the first to tenth triangles arranged as described above. 3. The method for producing a 32-hedral globe material described in 1. above.