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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 Cyclotruncated simplectic honeycomb ： ウィキペディア英語版 Cyclotruncated simplectic honeycomb In geometry, the cyclotruncated simplectic honeycomb (or cyclotruncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the $,\; and\; is\; represented\; by\; aCoxeter-Dynkin\; diagramas\; a\; cyclic\; graph\; of\; \text{'}\text{'}n+1\text{'}\text{'}\; nodes\; with\; two\; adjacent\; nodes\; ringed.\; It\; is\; composed\; of\; n-simplexfacets,\; along\; with\; alltruncatedn-simplices.$ It is also called a Kagome lattice in two and three dimensions, although it is not a lattice. In n-dimensions, each can be seen as a set of ''n+1'' sets of parallel hyperplanes that divide space. Each hyperplane contains the same honeycomb of one dimension lower. In 1-dimension, the honeycomb represents an apeirogon, with alternately colored line segments. In 2-dimensions, the honeycomb represents the trihexagonal tiling, with Coxeter graph . In 3-dimensions it represents the quarter cubic honeycomb, with Coxeter graph filling space with alternately tetrahedral and truncated tetrahedral cells. In 4-dimensions it is called a cyclotruncated 5-cell honeycomb, with Coxeter graph , with 5-cell, truncated 5-cell, and bitruncated 5-cell facets. In 5-dimensions it is called an cyclotruncated 5-simplex honeycomb, with Coxeter graph , filling space by 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets. In 6-dimensions it is called a cyclotruncated 6-simplex honeycomb, with Coxeter graph , filling space by 6-simplex, truncated 6-simplex, bitruncated 6-simplex, and tritruncated 6-simplex facets. }_1 !Apeirogon ! |120px Yellow and cyan line segments |- align=center !2 !$\}\_3$ !quarter cubic honeycomb !120px Elongated triangular antiprism |160px160px With yellow and blue tetrahedra, and red and purple truncated tetrahedra |- align=center !4 !$\}\_5$ !Cyclotruncated 5-simplex honeycomb !120px !5-simplex, truncated 5-simplex, bitruncated 5-simplex |- align=center !6 !$\}\_7$ !Cyclotruncated 7-simplex honeycomb ! !7-simplex, truncated 7-simplex, bitruncated 7-simplex |- align=center !8 !$$ == Projection by folding == The cyclotruncated (2''n''+1)- and 2''n''-simplex honeycombs and (2''n''-1)-simplex honeycombs can be projected into the n-dimensional hypercubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement: }_5 | !$\}\_9$ | !$$ | |... |- !$\}\_4$ | !$\}\_8$ | !$$ | |... |- ! | !$\}\_5$ | !$\}\_9$ | |... |- !$\}\_2$ | !$\}\_4$ | !$$ 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「Cyclotruncated simplectic 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.