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In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node branch. The rectified 231 is constructed by points at the mid-edges of the 231. These polytopes are part of a family of 127 (or 27−1) convex uniform polytopes in 7-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: . ==2_31 polytope== |- |bgcolor=#e7dcc3|5-faces||4788: 756 211 4032 |- |bgcolor=#e7dcc3|4-faces||16128: 4032 201 12096 |- |bgcolor=#e7dcc3|Cells||20160 |- |bgcolor=#e7dcc3|Faces||10080 |- |bgcolor=#e7dcc3|Edges||2016 |- |bgcolor=#e7dcc3|Vertices||126 |- |bgcolor=#e7dcc3|Vertex figure||131 25px |- |bgcolor=#e7dcc3|Petrie polygon||Octadecagon |- |bgcolor=#e7dcc3|Coxeter group||E7, () |- |bgcolor=#e7dcc3|Properties||convex |} The 231 is composed of 126 vertices, 2016 edges, 10080 faces (Triangles), 20160 cells (tetrahedra), 16128 4-faces (3-simplexes), 4788 5-faces (756 pentacrosses, and 4032 5-simplexes), 632 6-faces (576 6-simplexes and 56 221). Its vertex figure is a 6-demicube. Its 126 vertices represent the root vectors of the simple Lie group E7. This polytope is the vertex figure for a uniform tessellation of 7-dimensional space, 331. 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「2 31 polytope」の詳細全文を読む スポンサード リンク
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