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In geometry, the 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space. It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space. There are many different Wythoff constructions of this honeycomb.
In eight-dimensional Euclidean geometry, the cyclotruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, truncated 8-simplex, bitruncated 8-simplex, tritruncated 8-simplex, and quadritruncated 8-simplex facets. These facet types occur in proportions of 2:2:2:2:1 respectively in ...
8 lattice is the union of three A 8 lattices, and also identical to the E8 lattice. [3] ∪ ∪ = . The A * 8 lattice (also called A 9 8) is the union of nine A 8 lattices, and has the vertex arrangement of the dual honeycomb to the omnitruncated 8-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 8-simplex
In eight-dimensional Euclidean geometry, the omnitruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 8-simplex facets. The facets of all omnitruncated simplectic honeycombs are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the ...
The vertex arrangement of the 8-demicubic honeycomb is the D 8 lattice. [1] The 112 vertices of the rectified 8-orthoplex vertex figure of the 8-demicubic honeycomb reflect the kissing number 112 of this lattice. [2] The best known is 240, from the E 8 lattice and the 5 21 honeycomb.
8 colors In geometry , a hypercubic honeycomb is a family of regular honeycombs ( tessellations ) in n - dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group R n (or B ~ n –1 ) for n ≥ 3 .
The cyclotruncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated cube and octahedron cells, in a square antiprism vertex figure. It has a Coxeter diagram . Perspective view from center of octahedron. It can be seen as somewhat analogous to the trioctagonal tiling, which has truncated square and triangle ...
The FCC arrangement produces the tetrahedral-octahedral honeycomb. The HCP arrangement produces the gyrated tetrahedral-octahedral honeycomb . If, instead, every sphere is augmented with the points in space that are closer to it than to any other sphere, the duals of these honeycombs are produced: the rhombic dodecahedral honeycomb for FCC, and ...