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From Wikipedia, the free encyclopedia
In four-dimensional Euclidean geometry, the steric tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Steric tesseractic honeycomb | |
---|---|
(No image) | |
Type | Uniform honeycomb |
Schläfli symbol | h4{4,3,3,4} |
Coxeter-Dynkin diagram | = |
4-face type | {4,3,3} t0,3{4,3,3} {3,3,4} {3,3}×{} |
Cell type | {4,3} {3,3} {3}×{} |
Face type | {4} {3} |
Vertex figure | |
Coxeter group | = [4,3,31,1] |
Dual | ? |
Properties | vertex-transitive |
The [4,3,31,1], , Coxeter group generates 31 permutations of uniform tessellations, 23 with distinct symmetry and 4 with distinct geometry. There are two alternated forms: the alternations (19) and (24) have the same geometry as the 16-cell honeycomb and snub 24-cell honeycomb respectively.
B4 honeycombs | ||||
---|---|---|---|---|
Extended symmetry |
Extended diagram |
Order | Honeycombs | |
[4,3,31,1]: | ×1 | |||
<[4,3,31,1]>: ↔[4,3,3,4] |
↔ |
×2 | ||
[3[1+,4,3,31,1]] ↔ [3[3,31,1,1]] ↔ [3,3,4,3] |
↔ ↔ |
×3 | ||
[(3,3)[1+,4,3,31,1]] ↔ [(3,3)[31,1,1,1]] ↔ [3,4,3,3] |
↔ ↔ |
×12 |
Regular and uniform honeycombs in 4-space:
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