Cyclotruncated 7-simplex honeycomb

Cyclotruncated 7-simplex honeycomb
(No image)
TypeUniform honeycomb
FamilyCyclotruncated simplectic honeycomb
Schläfli symbolt0,1{3[8]}
Coxeter diagram
7-face types{36}
t0,1{36}
t1,2{36}
t2,3{36}
Vertex figureElongated 6-simplex antiprism
Symmetry×22, [[3[8]]]
Propertiesvertex-transitive

In seven-dimensional Euclidean geometry, the cyclotruncated 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, truncated 7-simplex, bitruncated 7-simplex, and tritruncated 7-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.

Structure

It can be constructed by eight sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 6-simplex honeycomb divisions on each hyperplane.

Related polytopes and honeycombs

This honeycomb is one of 29 unique uniform honeycombs[1] constructed by the Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:

See also

Regular and uniform honeycombs in 7-space:

Notes

  1. Weisstein, Eric W. "Necklace". MathWorld. , A000029 30-1 cases, skipping one with zero marks

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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