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In geometry, the truncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2. It has 120 vertices and 54 faces: 30 squares, 12 decagons, and 12 decagrams. The central region of the polyhedron is connected to the exterior via 20 small triangular holes. The name ''truncated dodecadodecahedron'' is somewhat misleading: truncation of the dodecadodecahedron would produce rectangular faces rather than squares, and the pentagram faces of the dodecahedron would turn into truncated pentagrams rather than decagrams. However, it is the quasitruncation of the dodecadodecahedron, as defined by .〔. See especially the description as a quasitruncation on p. 411 and the photograph of a model of its skeleton in Fig. 114, Plate IV.〕 For this reason, it is also known as the quasitruncated dodecadodecahedron.〔Wenninger writes "quasitruncated dodecahedron", but this appear to be a mistake. .〕 Coxeter et al. credit its discovery to a paper published in 1881 by Austrian mathematician Johann Pitsch.〔. According to , the truncated dodecadodecahedron appears as no. XII on p.86.〕 == Cartesian coordinates == Cartesian coordinates for the vertices of a truncated dodecadodecahedron are all the triples of numbers obtained by circular shifts and sign changes from the following points (where is the golden ratio): : Each of these five points has eight possible sign patterns and three possible circular shifts, giving a total of 120 different points. 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「Truncated dodecadodecahedron」の詳細全文を読む スポンサード リンク
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