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In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequences. The rectified 142 is constructed by points at the mid-edges of the 142 and is the same as the birectified 241, and the quadrirectified 421. These polytopes are part of a family of 255 (28 − 1) convex uniform polytopes in 8-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: . == 142 polytope == |- |bgcolor=#e7dcc3|5-faces||725760: 60480 112 181440 121 483840 |- |bgcolor=#e7dcc3|4-faces||2298240: 241920 102 604800 111 1451520 |- |bgcolor=#e7dcc3|Cells||3628800: 1209600 101 2419200 |- |bgcolor=#e7dcc3|Faces||2419200 |- |bgcolor=#e7dcc3|Edges||483840 |- |bgcolor=#e7dcc3|Vertices||17280 |- |bgcolor=#e7dcc3|Vertex figure||t2 25px |- |bgcolor=#e7dcc3|Petrie polygon||30-gon |- |bgcolor=#e7dcc3|Coxeter group||E8, () |- |bgcolor=#e7dcc3|Properties||convex |} The 142 is composed of 2400 facets: 240 132 polytopes, and 2160 7-demicubes (141). Its vertex figure is a birectified 7-simplex. This polytope, along with the demiocteract, can tessellate 8-dimensional space, represented by the symbol 152, and Coxeter-Dynkin 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「1 42 polytope」の詳細全文を読む スポンサード リンク
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