Symmetry Constructions
There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored 24-cell facets. In all cases, eight 24-cells meet at each vertex, but the vertex figures have different symmetry generators.
| Name | Coxeter group | Full symmetry group |
Coxeter-Dynkin diagram | Facets (24-cells) |
Vertex figure (8-cell) |
Vertex figure symmetry order |
|---|---|---|---|---|---|---|
| Regular 24-cell honeycomb | 8: | 384 | ||||
| Rectified 16-cell honeycomb | 6: 2: |
96 | ||||
| Birectified tesseractic honeycomb | ] | 4,4: | 64 | |||
| Rectified alternated tesseractic honeycomb | <> = | 2,2: 4: |
32 | |||
| Rectified quartered tesseractic honeycomb | ] = | 2,2,2,2: |
16 |
Read more about this topic: 24-cell Honeycomb
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