Cyclotruncated 6-simplex honeycomb

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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.

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×2, [[3[7]]]
Propertiesvertex-transitive

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.

Summarize
Perspective

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

More information , ...
A6 honeycombs
Heptagon
symmetry
Extended
symmetry
Extended
diagram
Extended
group
Honeycombs
a1 [3[7]]

i2 [[3[7]]] ×2

1

2

r14 [7[3[7]]] ×14

3

Close

See also

Regular and uniform honeycombs in 6-space:

Notes

References

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