Bi-icositetrareplenished grand hexacosichoron
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| Bi-icositetrareplenished grand hexacosichoron | |
|---|---|
| File:Bi-icositetrareplenished grand hexacosichoron.png | |
| Rank | 4 |
| Type | Scaliform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Birgax |
| Elements | |
| Cells | 48 trireplenished great icosahedra |
| Faces | 48+72 triangles, 72 pentagrams |
| Edges | 72+144 |
| Vertices | 72 |
| Vertex figure | Bi-trireplenished great icosahedron, edge lengths 1 and (√5-1)/2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Regiment | Birgax |
| Conjugate | Bi-icositetradiminished hexacosichoron |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | BC3+×12+, order 144 |
| Convex | No |
| Nature | Tame |
The bi-icositetrareplenished grand hexacosichoron, or birgax, is a nonconvex noble scaliform polychoron that consists of 48 trireplenished great icosahedra. Six cells join at each vertex.
It can be formed from the grand hexacosichoron in a similar way as its conjugate, the bi-icositetradiminished hexacosichoron, can be derived from the hexacosichoron, by removing 48 great icosahedral pyramids corresponding to the vertices of 2 inscribed great icosahedra. Removing only 1 set of 24 vertices instead results in the retrosnub disicositetrachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category S3: Special Scaliforms" (#S23).
- Klitzing, Richard. "birgax".