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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 Simplectic honeycomb ： ウィキペディア英語版 Simplectic honeycomb }_3 |- !Triangular tiling !Tetrahedral-octahedral honeycomb |- |120px With red and yellow equilateral triangles |160px With cyan and yellow tetrahedra, and red rectified tetrahedra (octahedron) |- ! ! |} In geometry, the simplectic honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the $,\; and\; is\; represented\; by\; aCoxeter-Dynkin\; diagramas\; a\; cyclic\; graph\; of\; \text{'}\text{'}n+1\text{'}\text{'}\; nodes\; with\; one\; node\; ringed.\; It\; is\; composed\; of\; n-simplexfacets,\; along\; with\; allrectifiedn-simplices.\; It\; can\; be\; thought\; of\; as\; an\; n-dimensionalhypercubic\; honeycombthat\; has\; been\; subdivided\; along\; all\; hyperplanes$ x+y+...\backslash in\backslash mathbb$,\; then\; stretched\; along\; its\; main\; diagonal\; until\; the\; simplices\; on\; the\; ends\; of\; the\; hypercubes\; become\; regular.\; Thevertex\; figureof\; an\; \text{'}\text{'}n-simplex\; honeycomb\text{'}\text{'}\; is\; anexpandedn-simplex.$ In 2 dimensions, the honeycomb represents the triangular tiling, with Coxeter graph filling the plane with alternately colored triangles. In 3 dimensions it represents the tetrahedral-octahedral honeycomb, with Coxeter graph filling space with alternately tetrahedral and octahedral cells. In 4 dimensions it is called the 5-cell honeycomb, with Coxeter graph , with 5-cell and rectified 5-cell facets. In 5 dimensions it is called the 5-simplex honeycomb, with Coxeter graph , filling space by 5-simplex, rectified 5-simplex, and birectified 5-simplex facets. In 6 dimensions it is called the 6-simplex honeycomb, with Coxeter graph , filling space by 6-simplex, rectified 6-simplex, and birectified 6-simplex facets. == By dimension == !Tessellation !Vertex figure !Facets per vertex figure !Vertices per vertex figure !Edge figure |- align=center |1 |$\}\_2$ | Triangular tiling 2-simplex honeycomb | Hexagon (Truncated triangle) |3+3 triangles |6 |Line segment |- align=center |3 |$\}\_4$ |4-simplex honeycomb |80px Runcinated 5-cell |5+5 5-cells 10+10 rectified 5-cells |20 |60px Triangular antiprism |- align=center |5 |$\}\_6$ |6-simplex honeycomb |80px Pentellated 6-simplex |7+7 6-simplex 21+21 rectified 6-simplex 35+35 birectified 6-simplex |42 |4-simplex antiprism |- align=center |7 |$\}\_8$ |8-simplex honeycomb |80px Heptellated 8-simplex |9+9 8-simplex 36+36 rectified 8-simplex 84+84 birectified 8-simplex 126+126 trirectified 8-simplex |72 |6-simplex antiprism |- align=center |9 |$\}\_$ |10-simplex honeycomb |80px Ennecated 10-simplex |11+11 10-simplex 55+55 rectified 10-simplex 165+165 birectified 10-simplex 330+330 trirectified 10-simplex 462+462 quadrirectified 10-simplex |110 |8-simplex antiprism |- align=center |11 |$$ |11-simplex honeycomb |... |... |... |... |} 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「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.