Cyclotruncated 6-simplex honeycomb

Cyclotruncated 6-simplex honeycomb
(No image)
TypeUniform honeycomb
FamilyCyclotruncated simplectic honeycomb
Schläfli symbolt0,1{3[7]}
Coxeter diagram
6-face types{35}
t{35}
2t{35}
3t{35}
Vertex figureElongated 5-simplex antiprism
Symmetry{\tilde{A}}_6×2, [[3[7]]]
Propertiesvertex-transitive

In six-dimensional Euclidean geometry, the cyclotruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 6-simplex, truncated 6-simplex, bitruncated 6-simplex, and tritruncated 6-simplex facets. These facet types occur in proportions of 2:2:2:1 respectively in the whole honeycomb.

Structure

It can be constructed by seven sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 5-simplex honeycomb divisions on each hyperplane.

Related polytopes and honeycombs

This honeycomb is one of 17 unique uniform honeycombs[1] constructed by the {\tilde{A}}_6 Coxeter group, grouped by their extended symmetry of the Coxeter–Dynkin diagrams:

See also

Regular and uniform honeycombs in 6-space:

Notes

  1. ↑

References

Fundamental convex regular and uniform honeycombs in dimensions 2–10
Family {\tilde{A}}_{n-1} {\tilde{C}}_{n-1} {\tilde{B}}_{n-1} {\tilde{D}}_{n-1} {\tilde{G}}_2 / {\tilde{F}}_4 / {\tilde{E}}_{n-1}
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 133 • 331
Uniform 9-honeycomb {3[9]} δ9 hδ9 qδ9 152 • 251 • 521
Uniform n-honeycomb {3[n]} δn hδn qδn 1k2 • 2k1 • k21
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