2 51 honeycomb

251 honeycomb
(No image)
TypeUniform tessellation
Family2k1 polytope
Schläfli symbol {3,3,35,1}
Coxeter symbol 251
Coxeter-Dynkin diagram
8-face types241
{37}
7-face types231
{36}
6-face types221
{35}
5-face types211
{34}
4-face type{33}
Cells{32}
Faces{3}
Edge figure051
Vertex figure151
Edge figure051
Coxeter group, [35,2,1]

In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation. It is composed of 241 polytope and 8-simplex facets arranged in an 8-demicube vertex figure. It is the final figure in the 2k1 family.

Construction

It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space.

The facet information can be extracted from its Coxeter-Dynkin diagram.

Removing the node on the short branch leaves the 8-simplex.

Removing the node on the end of the 5-length branch leaves the 241.

The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the 8-demicube, 151.

The edge figure is the vertex figure of the vertex figure. This makes the rectified 7-simplex, 051.

Related polytopes and honeycombs

References

Fundamental convex regular and uniform honeycombs in dimensions 3–10 (or 2-9)
Family / /
Uniform tiling {3[3]} δ3 hδ3 qδ3 Hexagonal
Uniform convex honeycomb {3[4]} δ4 hδ4 qδ4
Uniform 5-honeycomb {3[5]} δ5 hδ5 qδ5 24-cell honeycomb
Uniform 6-honeycomb {3[6]} δ6 hδ6 qδ6
Uniform 7-honeycomb {3[7]} δ7 hδ7 qδ7 222
Uniform 8-honeycomb {3[8]} δ8 hδ8 qδ8 133331
Uniform 9-honeycomb {3[9]} δ9 hδ9 qδ9 152251521
Uniform 10-honeycomb {3[10]} δ10 hδ10 qδ10
Uniform n-honeycomb {3[n]} δn hδn qδn 1k22k1k21
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