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8-demicube Honeycomb
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. The 112 vertices of the rectified 8-orthoplex vertex figure of the ''8-demicubic honeycomb'' reflect the kissing number 112 of this lattice. The best known is 240, from the E8 lattice and the 521 honeycomb. _8 contains _8 as a subgroup of index 270. Both _8 and _8 can be seen as affine extensions of D_8 from different nodes: 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 n8). It is identical to the E8 lattice. At 8-dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform 8-honeycomb
In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope Ridge (geometry), ridge being shared by exactly two 8-polytope Facet (mathematics), facets. A uniform 9-polytope is one which is vertex-transitive, and constructed from uniform 8-polytope Facet (geometry), facets. Regular 9-polytopes Regular 9-polytopes can be represented by the Schläfli symbol , with w 8-polytope Facet (mathematics), facets around each Peak (geometry), peak. There are exactly three such List of regular polytopes#Convex 4, convex regular 9-polytopes: # - 9-simplex # - 9-cube # - 9-orthoplex There are no nonconvex regular 9-polytopes. Euler characteristic The topology of any given 9-polytope is defined by its Betti numbers and torsion coefficient (topology), torsion coefficients.Richeson, D.; ''Euler's Gem: The Polyhedron Formula and the Birth of Topoplogy'', Princeton, 2008. The value of the Euler characteristic used t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
