に切稜立方体を加えた木製多面体のセットです。

fig.1fig.2

fig.3fig.4

fig.5fig.6

fig.7fig.8

fig.9fig.10

fig.11fig.12

fig.13fig.14

fig.15fig.16

fig.17fig.18

fig.19fig.20

fig.21fig.22

fig.23fig.24

fig.25fig.26

fig.27fig.28

(The chamfered cube often appears to be a prototype in the hand-made modelling from the wooden cube to various polyhedra.)

Ikuro SATO

The wooden polyhedra are composed of 30 pieces shown in figures, including 5 Platonic(Fig 1-5), 16 Archimedean(Fig 6-19), 6 Catalan(Fig 20-25), 2 Fedrov(Fig 26-27) and the chamfered cube(Fig 28).

About the chamfered cube(Fig 28), this is the most favorite solid of him, because the chamfered cube often appears to be a prototype in the hand-made modeling from the wood cube to various polyhedra.

He hopes and believes that the wooden polyhedra are useful for the students to entertain, inform and teach some mathematics. But, his interest is not limited in hand-made modeling of wooden polyhedra. He is interested in surprisingly wide topics. Especially, I want to introduce a recent episode of the collaborative study of NAKAGAWA and J. AKIYAMA.

In June 2008 an international congress was held in Moscow for celebrating the 100 years anniversary of birth of the Russian mathematician L. S. Pontrjagin. In this congress a Japanese mathematician J. Akiyama made a lecture on the set and the element number of parallelohedra, "New theorem about parallelohedra".

Fedorov's parallelopolyhedra are defined as polyhedra with the following conditions:

a. each face has a parallel counterpart,

b. each edge belong to a group of parallel edges,

c. repetition of the same polyhedra must fill the space to produce a translation symmetry only (neither rotation nor reflection).

These polyhedra are limited to the five members consisting of cube(Fig 2), truncated octahedron(Fig 8), rhombic dodecahedron(Fig 24), hexagonal prism(Fig 26) and elongated rhombic dodecahedron(Fig 27). These polyhedra are less popular than the Platonic bodies, but are considered equally important because they play a role of space packing.

Now, let us consider the problem "what is a space-tessellation producer?", i.e. what is an elementary body producing space filling bodies?". General proof of this problem is quite difficult, but simple examples are found as follows.

We can construct all of the parallelopolyhedra with one kind of element, where its mirror image is looked upon as the same one. Let the element be denoted by σ, then the cube is constructed by 96 elements of one kind (σ96), the hexagonal prism is σ144, the rhombic dodecahedron is σ192, the elongated rhombic dodecahedron is σ384 and the truncated octahedron is σ48.

fig.30

Fig.29 The pentahedron σ is an atom building up all of the 5 types of Fedorov's polyhedra, whose development is shown in Fig.30.

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Price list

WOODEN POLYHEDRA 5Platonic solids set(Fig 1-5) with tray ; $30US including shipping

＝23euro including shipping＝\2,750（トレー、送料込）

WOODEN POLYHEDRA 20(Platonic & Archmedean solids set in case including shipping);$300US＝270euro＝\30,000（箱入、送料込）

WOODEN POLYHEDRA 30(Platonic, Archmedean, Catalan & Fedrov solids set in case including shipping);$500US＝460euro＝\49,980（箱入、送料込）

One piece price($1usd=1.1euro=\115yen)

fig.1:正４面体tetrahedron=\400

fig.2:立方体cube=\100

fig.3:正８面体octahedron=\400

fig.4:正１２面体dodecahedron=\500

fig.5:正２０面体icosahedron=\600

fig.6:切頂４面体truncated tetrahedron=\500

fig.7:切頂立方体truncated cube=\500

fi fig.9:切頂１２面体truncated dodecahedron=\1,000

fig.10:切頂２０面体truncated icosahedron=\1,000

fig.11:立方８面体cub-octahedron=\500

fig.12:小菱形立方８面体rhomb-cub-octahedron=\800

fig.13:ミラーの立体Miller's solid=\800

fig.14:大菱形立方８面体great rhomb-cub-octahedron=\800

fig.15:ねじれ立方体snub cube=\1,200

fig.16:２０・１２面体icosi-dodecahedron=\1,000

fig.17:小菱形２０・１２面体rhomb-icosi-dodecahedron=\3,000

fig.18:大菱形２０・１２面体great rhomb-icosi-dodecahedron=\3,000

fig.19:ねじれ１２面体snub dodecahedron=\5,000

fig.20:三方四面体triakis tetrahedron=\2,000

fig.21:三方八面体triakis octahedron=\2,000

fig.22:四方六面体tetrakis hexahedron=\2,000

fig.23:凧型２４面体deltoidal icositetrahedron=\2,400

fig.24:菱形１２面体rhombic dodecahedron=\1,000

fig.25:菱形３０面体rhombic triacontahedron=\3,000

fig.26:六角柱hexagonal prism=\600

fig.27:長菱形１２面体elongated rhombic dodecahedron=\800

fig.28:切稜立方体chamfered cube=\500

fig.29:ペンタドロンPentadron=\500

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