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In geometry, a tetrahedrally diminished〔It is also less accurately called a tetrahedrally truncated dodecahedron〕 dodecahedron (also tetrahedrally stellated icosahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals).〔(Tetrahedrally Stellated Icosahedron )〕 It has chiral tetrahedral symmetry, and so its geometry can be constructed from pyritohedral symmetry of the pseudoicosahedron with 4 faces stellated, or from the pyritohedron, with 4 vertices diminished. Within its tetrahedral symmetry, it has geometric varied proportions. By Dorman Luke dual construction, a unique geometric proportion can be defined. The kite faces have edges of length ratio ~ 1:0.6325. As a self-dual hexadecahedron, it is one of 302404 forms, 1476 with at least order 2 symmetry, and the only one with tetrahedral symmetry.〔(Self-Dual Hexadecahedra )〕 As a diminished regular dodecahedron, with 4 vertices removed, the quadrilaterals faces are trapezoids. As a stellation of the regular icosahedron it is one of 32 stellations defined with tetrahedral symmetry. It has kite faces.〔(Tetrahedral Stellations of the Icosahedron )〕 In Conway polyhedron notation, it can represented as pT, applying George W. Hart's propeller operator to a regular tetrahedron.〔(Conway Notation for Polyhedra )〕 == Related polytopes and honeycombs== This polyhedron represents the vertex figure of a hyperbolic uniform honeycomb, the partially diminished icosahedral honeycomb, pd, with 12 pentagonal antiprisms and 4 dodecahedron cells meeting at every vertex. :120px :Vertex figure projected as Schlegel diagram 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「Tetrahedrally diminished dodecahedron」の詳細全文を読む スポンサード リンク
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