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8-cube honeycomb : ウィキペディア英語版
8-cubic honeycomb

t0,8
8
|-
|bgcolor=#e7dcc3|Coxeter-Dynkin diagrams||
|-
|bgcolor=#e7dcc3|8-face type||
|-
|bgcolor=#e7dcc3|7-face type||
|-
|bgcolor=#e7dcc3|6-face type||
|-
|bgcolor=#e7dcc3|5-face type||
|-
|bgcolor=#e7dcc3|4-face type||
|-
|bgcolor=#e7dcc3|Cell type||
|-
|bgcolor=#e7dcc3|Face type||
|-
|bgcolor=#e7dcc3|Face figure||
(octahedron)
|-
|bgcolor=#e7dcc3|Edge figure||8
(16-cell)
|-
|bgcolor=#e7dcc3|Vertex figure||256
(8-orthoplex)
|-
|bgcolor=#e7dcc3|Coxeter group||()
|-
|bgcolor=#e7dcc3|Dual||self-dual
|-
|bgcolor=#e7dcc3|Properties||vertex-transitive, edge-transitive, face-transitive, cell-transitive
|}
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. The most symmetric form is regular, with Schläfli symbol . Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol . The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol 8.
== Related honeycombs ==
The (), , Coxeter group generates 511 permutations of uniform tessellations, 271 with unique symmetry and 270 with unique geometry. The expanded 8-cubic honeycomb is geometrically identical to the 8-cubic honeycomb.
The ''8-cubic honeycomb'' can be alternated into the 8-demicubic honeycomb, replacing the 8-cubes with 8-demicubes, and the alternated gaps are filled by 8-orthoplex facets.

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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