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In geometry, 2k1 polytope is a uniform polytope in ''n'' dimensions (''n'' = ''k''+4) constructed from the En Coxeter group. The family was named by their Coxeter symbol as 2k1 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequence. It can be named by an extended Schläfli symbol . == Family members == The family starts uniquely as 6-polytopes, but can be extended backwards to include the 5-orthoplex (pentacross) in 5-dimensions, and the 4-simplex (5-cell) in 4-dimensions. Each polytope is constructed from (n-1)-simplex and 2k-1,1 (n-1)-polytope facets, each has a vertex figure as an (n-1)-demicube, '. The sequence ends with k=6 (n=10), as an infinite hyperbolic tessellation of 9-space. The complete family of 2k1 polytope polytopes are: # 5-cell: 201, (5 tetrahedra cells) # Pentacross: 211, (32 5-cell (201) facets) # 221, (72 5-simplex and 27 5-orthoplex (211) facets) # 231, (576 6-simplex and 56 221 facets) # 241, (17280 7-simplex and 240 231 facets) # 251, tessellates Euclidean 8-space (∞ 8-simplex and ∞ 241 facets) # 261, tessellates hyperbolic 9-space (∞ 9-simplex and ∞ 251 facets) 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「uniform 2 k1 polytope」の詳細全文を読む スポンサード リンク
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