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h |- |bgcolor=#e7dcc3|Vertex figure||Rectified heptacross |- |bgcolor=#e7dcc3|Coxeter group||, () |} The 7-demicubic honeycomb, or demihepteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 7-space. It is constructed as an alternation of the regular 7-cubic honeycomb. It is composed of two different types of facets. The 7-cubes become alternated into 7-demicubes h and the alternated vertices create 7-orthoplex facets. == D7 lattice == The vertex arrangement of the 7-demicubic honeycomb is the D7 lattice.〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/D7.html〕 The 84 vertices of the rectified 7-orthoplex vertex figure of the ''7-demicubic honeycomb'' reflect the kissing number 84 of this lattice.〔''Sphere packings, lattices, and groups'', by John Horton Conway, Neil James Alexander Sloane, Eiichi Bannai ()〕 The best known is 126, from the E7 lattice and the 331 honeycomb. The D packing (also called D) can be constructed by the union of two ''D7 lattices''. The D packings form lattices only in even dimensions. The kissing number is 26=64 (2n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8).〔Conway (1998), p. 119〕 : ∪ The D lattice (also called D and C) can be constructed by the union of all four 7-demicubic lattices:〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds7.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 14 (''2n'' for n≥5) and its Voronoi tessellation is a quadritruncated 7-cubic honeycomb, , containing all with tritruncated 7-orthoplex, Voronoi cells.〔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「7-demicubic honeycomb」の詳細全文を読む スポンサード リンク
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