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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク E9 honeycomb ： ウィキペディア英語版 E9 honeycomb In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. $\{\backslash bar\{T\}\}\_9$, also (E10) is a paracompact hyperbolic group, so either facets or vertex figures will not be bounded. E10 is last of the series of Coxeter groups with a bifurcated Coxeter-Dynkin diagram of lengths 6,2,1. There are 1023 unique E10 honeycombs by all combinations of its Coxeter-Dynkin diagram. There are no regular honeycombs in the family since its Coxeter diagram is a nonlinear graph, but there are three simplest ones, with a single ring at the end of its 3 branches: 621, 261, 162. ==621 honeycomb== |- |bgcolor=#e7dcc3|8-faces|| |- |bgcolor=#e7dcc3|7-faces|| |- |bgcolor=#e7dcc3|6-faces|| |- |bgcolor=#e7dcc3|5-faces|| |- |bgcolor=#e7dcc3|4-faces|| |- |bgcolor=#e7dcc3|Cells|| |- |bgcolor=#e7dcc3|Faces|| |- |bgcolor=#e7dcc3|Vertex figure||521 |- |bgcolor=#e7dcc3|Symmetry group||$$ The 621 honeycomb is constructed from alternating 9-simplex and 9-orthoplex facets within the symmetry of the E10 Coxeter group. This honeycomb is highly regular in the sense that its symmetry group (the affine E9 Weyl group) acts transitively on the ''k''-faces for ''k'' ≤ 7. All of the ''k''-faces for ''k'' ≤ 8 are simplices. This honeycomb is last in the series of k21 polytopes, enumerated by Thorold Gosset in 1900, listing polytopes and honeycombs constructed entirely of regular facets, although his list ended with the 8-dimensional the Euclidean honeycomb, 521.〔Conway, 2008, The Gosset series, p 413〕 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「E9 honeycomb」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.