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In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα ''dōdeka'' "twelve" + ἕδρα ''hédra'' "base", "seat" or "face") is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120. The pyritohedron is an irregular pentagonal dodecahedron, having the same topology as the regular one but pyritohedral symmetry while the tetaroid has tetrahedral symmetry. The rhombic dodecahedron, seen as a limiting case of the pyritohedron has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra are space-filling. There are a large number of other dodecahedra. ==Pentagonal dodecahedron== (詳細はPlatonic solids and can be represented by its Schläfli symbol . The dual polyhedron is the regular icosahedron , having five equilateral triangles around each vertex. In crystallography, two important dodecahedra can occur as crystal forms in some symmetry classes of the cubic crystal system that are topologically equivalent to the regular dodecahedron but less symmetrical: the pyritohedron with pyritohedral symmetry, and the tetartoid with tetrahedral symmetry: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dodecahedron」の詳細全文を読む スポンサード リンク
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