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}.
Read more about this topic: 3 31 Honeycomb
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