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E7 honeycomb : ウィキペディア英語版
3 31 honeycomb


|-
|bgcolor=#e7dcc3|6-face types||221

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|bgcolor=#e7dcc3|5-face types||211

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|bgcolor=#e7dcc3|4-face type||
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|bgcolor=#e7dcc3|Cell type||
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|bgcolor=#e7dcc3|Face type||
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|bgcolor=#e7dcc3|Face figure||031 25px
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|bgcolor=#e7dcc3|Edge figure||131 25px
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|bgcolor=#e7dcc3|Vertex figure||231 25px
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|bgcolor=#e7dcc3|Coxeter group||
In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.
==Construction==

It is created by a Wythoff construction upon a set of 8 hyperplane mirrors in 7-dimensional space.
The facet information can be extracted from its Coxeter-Dynkin diagram.
:
Removing the node on the short branch leaves the 6-simplex facet:
:
Removing the node on the end of the 3-length branch leaves the 321 facet:
:
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes 231 polytope.
:
The edge figure is determined by removing the ringed node and ringing the neighboring node. This makes 6-demicube (131).
:
The face figure is determined by removing the ringed node and ringing the neighboring node. This makes rectified 5-simplex (031).
:
The cell figure is determined by removing the ringed node of the face figure and ringing the neighboring nodes. This makes tetrahedral prism {}×{3,3}.
:

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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