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Euclidean Geometry, 8-dimensional: Cyclotruncated 8-simplex From Wikipedia, the free encyclopedia
In eight-dimensional Euclidean geometry, the cyclotruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, truncated 8-simplex, bitruncated 8-simplex, tritruncated 8-simplex, and quadritruncated 8-simplex facets. These facet types occur in proportions of 2:2:2:2:1 respectively in the whole honeycomb.
Cyclotruncated 8-simplex honeycomb | |
---|---|
(No image) | |
Type | Uniform honeycomb |
Family | Cyclotruncated simplectic honeycomb |
Schläfli symbol | t0,1{3[9]} |
Coxeter diagram | |
8-face types | {37} , t0,1{37} t1,2{37} , t2,3{37} t3,4{37} |
Vertex figure | Elongated 7-simplex antiprism |
Symmetry | ×2, [[3[9]]] |
Properties | vertex-transitive |
It can be constructed by nine sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 7-simplex honeycomb divisions on each hyperplane.
This honeycomb is one of 45 unique uniform honeycombs[1] constructed by the Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:
A8 honeycombs | ||||
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Enneagon symmetry |
Symmetry | Extended diagram |
Extended group |
Honeycombs |
a1 | [3[9]] |
| ||
i2 | [[3[9]]] | ×2 |
| |
i6 | [3[3[9]]] | ×6 | ||
r18 | [9[3[9]]] | ×18 | 3 |
Regular and uniform honeycombs in 8-space:
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