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In geometry, 1k2 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 1k2 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-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-demicube (demipenteract) in 5-dimensions, and the 4-simplex (5-cell) in 4-dimensions. Each polytope is constructed from 1k-1,2 and (n-1)-demicube facets. Each has a vertex figure of a ' polytope is a birectified n-simplex, ''t2''. The sequence ends with k=6 (n=10), as an infinite tessellation of 9-dimensional hyperbolic space. The complete family of 1k2 polytope polytopes are: # 5-cell: 102, (5 tetrahedral cells) # 112 polytope, (16 5-cell, and 10 16-cell facets) # 122 polytope, (54 demipenteract facets) # 132 polytope, (56 122 and 126 demihexeract facets) # 142 polytope, (240 132 and 2160 demihepteract facets) # 152 honeycomb, tessellates Euclidean 8-space (∞ 142 and ∞ demiocteract facets) # 162 honeycomb, tessellates hyperbolic 9-space (∞ 152 and ∞ demienneract 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 1 k2 polytope」の詳細全文を読む スポンサード リンク
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