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h |- |bgcolor=#e7dcc3|Vertex figure||Rectified octacross |- |bgcolor=#e7dcc3|Coxeter group|| () |} The 8-demicubic honeycomb, or demiocteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 8-space. It is constructed as an alternation of the regular 8-cubic honeycomb. It is composed of two different types of facets. The 8-cubes become alternated into 8-demicubes h and the alternated vertices create 8-orthoplex facets . == D8 lattice == The vertex arrangement of the 8-demicubic honeycomb is the D8 lattice.〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/D8.html〕 The 112 vertices of the rectified 8-orthoplex vertex figure of the ''8-demicubic honeycomb'' reflect the kissing number 112 of this lattice.〔''Sphere packings, lattices, and groups'', by John Horton Conway, Neil James Alexander Sloane, Eiichi Bannai ()〕 The best known is 240, from the E8 lattice and the 521 honeycomb. as a subgroup of index 270.〔Johnson (2015) p.177〕 Both can be seen as affine extensions of from different nodes: File:Affine D8 E8 relations.png The D lattice (also called D) can be constructed by the union of two D8 lattices. This packing is only a lattice for even dimensions. The kissing number is 240. (2n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8).〔Conway (1998), p. 119〕 It is identical to the E8 lattice. At 8-dimensions, the 240 contacts contain both the 27=128 from lower dimension contact progression (2n-1), and 16 *7=112 from higher dimensions (2n(n-1)). : ∪ = . The D lattice (also called D and C) can be constructed by the union of all four ''D8 lattices'':〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds8.html〕 It is also the 7-dimensional body centered cubic, the union of two 7-cube honeycombs in dual positions. : ∪ ∪ ∪ = ∪ . The kissing number of the D lattice is 16 (''2n'' for n≥5).〔Conway (1998), p. 120〕 and its Voronoi tessellation is a quadrirectified 8-cubic honeycomb, , containing all trirectified 8-orthoplex Voronoi cell, .〔Conway (1998), p. 466〕 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「8-demicubic honeycomb」の詳細全文を読む スポンサード リンク
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