Noble octagrammic icositetrahedron
(Redirected from Noble faceting of great rhombicuboctahedron)
| Noble octagrammic icositetrahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Noble |
| Elements | |
| Faces | 24 mirror-symmetric octagrams |
| Edges | 24+24+48 |
| Vertices | 48 |
| Vertex figure | 48 irregular tetragons |
| Number of external pieces | 168 |
| Level of complexity | 28 |
| Related polytopes | |
| Army | Semi-uniform great rhombicuboctahedron |
| Dual | Noble tetragonal tetracontoctahedron |
| Convex core | Non-Catalan tetrakis hexahedron |
| Abstract & topological properties | |
| Flag count | 384 |
| Euler characteristic | –24 |
| Schläfli type | {8,4} |
| Orientable | Yes |
| Genus | 13 |
| Properties | |
| Symmetry | B3, order 48 |
| Flag orbits | 8 |
| Convex | No |
| Nature | Tame |
| History | |
| Discovered by | Plasmath |
| First discovered | 2023 |
The noble octagrammic icositetrahedron is a noble polyhedron. Its 24 congruent faces are mirror-symmetric octagrams meeting at congruent order-4 vertices. It is a faceting of a semi-uniform great rhombicuboctahedral convex hull.
The ratio between the longest and shortest edges is 1:a ≈ 1:1.19166, where a is the positive real root of .
Vertex coordinates[edit | edit source]
This polyhedron's vertex coordinates are given by all permutations and sign changes of
- (1, a, b),
where
- , and
- .
![{\displaystyle a=\frac{\sqrt[3]{188+12\sqrt{93}}+\sqrt[3]{188-12\sqrt{93}}+5}{6}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee1f91ad0a9270b6cf1cffb19497aa7e0c4ac11)
![{\displaystyle b=\frac{\sqrt[3]{188+12\sqrt{93}}+\sqrt[3]{188-12\sqrt{93}}+\sqrt[3]{116+12\sqrt{93}}+\sqrt[3]{116-12\sqrt{93}}+7}{6}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/393be01d321ef45f2038feeb3c2ce9dfabe9f2cd)