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5-simplex honeycomb : ウィキペディア英語版
5-simplex honeycomb
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t2 30px
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|bgcolor=#e7dcc3|Vertex figure||t0,4 30px
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In five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of 2:2:1 respectively in the whole honeycomb.
== A5 lattice ==
This vertex arrangement is called the A5 lattice or 5-simplex lattice. The 30 vertices of the stericated 5-simplex vertex figure represent the 30 roots of the {\tilde{A}}_5 Coxeter group.〔http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A5.html〕 It is the 5-dimensional case of a simplectic honeycomb.
The A lattice can be constructed as the union of two A5 lattices:
:

The A is the union of three A5 lattices:
:
∪ ∪ .
The A lattice (also called A) is the union of six A5 lattices, and is the dual vertex arrangement to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-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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