Small hecatonicosintercepted hecatonicosachoron
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| Small hecatonicosintercepted hecatonicosachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Shinhi |
| Elements | |
| Cells | 120 icosidodecahedra, 120 truncated dodecahedra |
| Faces | 2400 triangles, 720 pentagons, 720 decagons |
| Edges | 3600 |
| Vertices | 1200 |
| Vertex figure | Triangular toroprism, edge lengths 1 (base edges), (1+√5)/2 (side edges of rectangles), and √(5+√5)/2 (side edges of triangles) |
| Edge figure | id 5 id 3 tid 10 tid 10 tid 3 |
| Measures (edge length 1) | |
| Circumradius | |
| Hypervolume | |
| Dichoral angles | Id–5–id: 144° |
| Id–3–tid: 120° | |
| Tid–10–tid: 60° | |
| Number of pieces | 2520 |
| Level of complexity | 6 |
| Related polytopes | |
| Army | Rahi |
| Regiment | Rahi |
| Conjugate | Great hecatonicosintercepted hecatonicosachoron |
| Convex core | Hecatonicosachoron |
| Abstract properties | |
| Euler characteristic | 1200 |
| Topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | H4, order 14400 |
| Convex | No |
| Nature | Wild |
The small hecatonicosintercepted hecatonicosachoron, or shinhi, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra and 120 truncated dodecahedra. 3 icosidodecahedra and 6 truncated dodecahedra join at each vertex.
It is wild because it has icosidodecahedra intercepted by decagons.
Gallery[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the rectified hecatonicosachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 3: Triangular Rectates" (#50).
- Klitzing, Richard. "shinhi".