quarter 5-cubic honeycomb | |
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(No image) | |
Type | Uniform 5-honeycomb |
Family | Quarter hypercubic honeycomb |
Schläfli symbol | q{4,3,3,3,4} |
Coxeter-Dynkin diagram | = |
5-face type | h{4,33}, h4{4,33}, |
Vertex figure | Rectified 5-cell antiprism or Stretched birectified 5-simplex |
Coxeter group | ×2 = [[31,1,3,31,1]] |
Dual | |
Properties | vertex-transitive |
In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 5-demicubic honeycomb, and a quarter of the vertices of a 5-cube honeycomb.[1] Its facets are 5-demicubes and runcinated 5-demicubes.
This honeycomb is one of 20 uniform honeycombs constructed by the Coxeter group, all but 3 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 20 permutations are listed with its highest extended symmetry relation:
D5 honeycombs | |||
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Extended symmetry |
Extended diagram |
Extended group |
Honeycombs |
[31,1,3,31,1] | |||
<[31,1,3,31,1]> ↔ [31,1,3,3,4] |
↔ |
×21 = | , , ,
, , , |
[[31,1,3,31,1]] | ×22 | , | |
<2[31,1,3,31,1]> ↔ [4,3,3,3,4] |
↔ |
×41 = | , , , , , |
[<2[31,1,3,31,1]>] ↔ [[4,3,3,3,4]] |
↔ |
×8 = ×2 | , , |