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25px h 25px |- |bgcolor=#e7dcc3|Vertex figure||t1 25px |- |bgcolor=#e7dcc3|Coxeter group|| () |} The 6-demicubic honeycomb or demihexeractic honeycube is a uniform space-filling tessellation (or honeycomb) in Euclidean 6-space. It is constructed as an alternation of the regular 6-cube honeycomb. It is composed of two different types of facets. The 6-cubes become alternated into 6-demicubes h and the alternated vertices create 6-orthoplex facets. == D6 lattice == The vertex arrangement of the 6-demicubic honeycomb is the D6 lattice.〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/D6.html〕 The 60 vertices of the rectified 6-orthoplex vertex figure of the ''6-demicubic honeycomb'' reflect the kissing number 60 of this lattice.〔''Sphere packings, lattices, and groups'', by John Horton Conway, Neil James Alexander Sloane, Eiichi Bannai ()〕 The best known is 72, from the E6 lattice and the 222 honeycomb. The D lattice (also called D) can be constructed by the union of two D6 lattices. This packing is only a lattice for even dimensions. The kissing number is 25=32 (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 6-demicubic lattices:〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds6.html〕 It is also the 6-dimensional body centered cubic, the union of two 6-cube honeycombs in dual positions. : ∪ ∪ ∪ = ∪ . The kissing number of the D6 * lattice is 12 (''2n'' for n≥5).〔Conway (1998), p. 120〕 and its Voronoi tessellation is a trirectified 6-cubic honeycomb, , containing all birectified 6-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「6-demicubic honeycomb」の詳細全文を読む スポンサード リンク
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