Gourt Home::Gourt :: Snub 24-cell
| (No image) | |
| Type | Uniform polychoron |
| Cells | 120 3.3.3 24 3.3.3.3.3 |
| Faces | 480 {3} |
| Edges | 432 |
| Vertices | 96 |
| Vertex configuration | 5 3.3.3 3 3.3.3.3.3 (Tridiminished icosahedron) |
| Symmetry group | -- |
| Properties | convex |
It is one of three semiregular polychora made two or more cells which are platonic solids.
Names:
- Snub icositetrachoron
- Snub 24-cell
- Snub polyoctahedron
- Sadi (Jonathan Bowers: for snub disicositetrachoron)
The vertices of a snub 24-cell centered at the origin of 4-space, with edges of length 2, are obtained by taking even permutations of
- (0, ±1, ±φ, ±φ2)
(where φ = (1+√5)/2 is the golden ratio).
These 96 vertices can be found by partitioning each of the 96 edges of a 24-cell into the golden ratio in a consistent manner, in much the same way that the 12 vertices of an icosahedron or "snub octahedron" can be produced by partitioning the 12 edges of an octahedron in the golden ratio. This is done by first placing vectors along the 24-cell's edges such that each two-dimensional face is bounded by a cycle, then similarly partitioning each edge into the golden ratio along the direction of its vector. The 96 vertices of the snub 24-cell, together with the 24 vertices of a 24-cell, form the 120 vertices of the 600-cell.
External links
"Snub 24-cell"