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8-simplex honeycomb
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8-simplex honeycomb : ウィキペディア英語版
8-simplex honeycomb
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In eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, rectified 8-simplex, birectified 8-simplex, and trirectified 8-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.
== A8 lattice ==
This vertex arrangement is called the A8 lattice or 8-simplex lattice. The 72 vertices of the expanded 8-simplex vertex figure represent the 72 roots of the }_8 contains }_8 and {\tilde{A}}_8 can be seen as affine extensions of A_8 from different nodes: File:Affine A8 E8 relations.png
The A lattice is the union of three A8 lattices, and also identical to the E8 lattice.
: ∪ ∪ = .
The A lattice (also called A) is the union of nine A8 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
:








= dual of .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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