| bgcolor=#e7dcc3 colspan=2 | Snub 24-cell honeycomb | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | (No image) | |
| Type | Uniform 4-honeycomb | |
| Schläfli symbols | s sr 2sr 2sr s | |
| Coxeter diagrams | = | |
| 4-face type | ||
| Cell type | ||
| Face type | ||
| Vertex figure | Irregular decachoron | |
| Symmetries | [3<sup>+</sup>,4,3,3] [3,4,(3,3)<sup>+</sup>] [4,(3,3)<sup>+</sup>,4] [4,(3,3<sup>1,1</sup>)<sup>+</sup>] [3<sup>1,1,1,1</sup>]+ | |
| Properties | Vertex transitive, nonWythoffian |
It can be seen as an alternation of a truncated 24-cell honeycomb, and can be represented by Schläfli symbol s, s, and 3 other snub constructions.
It is defined by an irregular decachoron vertex figure (10-celled 4-polytope), faceted by four snub 24-cells, one 16-cell, and five 5-cells. The vertex figure can be seen topologically as a modified tetrahedral prism, where one of the tetrahedra is subdivided at mid-edges into a central octahedron and four corner tetrahedra. Then the four side-facets of the prism, the triangular prisms become tridiminished icosahedra.
There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored snub 24-cell, 16-cell, and 5-cell facets. In all cases, four snub 24-cells, five 5-cells, and one 16-cell meet at each vertex, but the vertex figures have different symmetry generators.
| Symmetry | Coxeter Schläfli | Facets (on vertex figure) | ||
|---|---|---|---|---|
| Snub 24-cell (4) | 16-cell (1) | 5-cell (5) | ||
| [3<sup>+</sup>,4,3,3] | s | 4: | ||
| [3,4,(3,3)<sup>+</sup>] | sr | 3: 1: | ||
| [[4,(3,3)+,4]] | 2sr | 2,2: | ||
| [(3<sup>1,1</sup>,3)<sup>+</sup>,4] | 2sr | 1,1: 2: | ||
| [3<sup>1,1,1,1</sup>]+ | s | 1,1,1,1: | ||
Regular and uniform honeycombs in 4-space: