First noble kipiscoidal icositetrahedron
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| First noble kipiscoidal icositetrahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Noble |
| Elements | |
| Faces | 24 irregular pentagons |
| Edges | 12+24+24 |
| Vertices | 24 |
| Vertex figure | Irregular pentagon |
| Number of external pieces | 72 |
| Level of complexity | 22 |
| Related polytopes | |
| Army | Snub cube |
| Dual | First noble kipiscoidal icositetrahedron |
| Convex core | Pentagonal icositetrahedron |
| Abstract & topological properties | |
| Flag count | 240 |
| Euler characteristic | –12 |
| Orientable | Yes |
| Genus | 7 |
| Properties | |
| Symmetry | B3+, order 24 |
| Flag orbits | 10 |
| Convex | No |
| Nature | Tame |
The noble faceting of the snub cube, or the first noble kipiscoidal icositetrahedron, is a self-dual noble polyhedron. Its 24 congruent faces are irregular pentagons meeting at congruent order-5 vertices.
The ratio between the longest and shortest edges is 1:a ≈ 1:1.68502, where a is the positive real root of a6-4a4+4a2-2.
This was the first noble polyhedron discovered in more than 100 years since Max Brückner studied such figures, by Robert Webb.
Bibliography[edit | edit source]
- Webb, Robert (2008). "Noble Faceting of Snub Cube". Stella.