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 | |
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(No image) | |
Type | Uniform honeycomb |
Family | Cyclotruncated simplectic honeycomb |
Schläfli symbol | t0,1{3[7]} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-face types | {35} ![]() t{35} ![]() 2t{35} ![]() 3t{35} ![]() |
Vertex figure | Elongated 5-simplex antiprism |
Symmetry | ×2, [[3[7]]] |
Properties | vertex-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.
Related polytopes and honeycombs
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:
A6 honeycombs | ||||
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Heptagon symmetry |
Extended symmetry |
Extended diagram |
Extended group |
Honeycombs |
a1 | [3[7]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
| |
i2 | [[3[7]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×2 | |
r14 | [7[3[7]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×14 |
See also
Regular and uniform honeycombs in 6-space:
Notes
References
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