Great hexacosifaceted trishecatonicosachoron
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| Great hexacosifaceted trishecatonicosachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Gaxifthi |
| Elements | |
| Cells | 120 dodecahedra, 120 quasitruncated great stellated dodecahedra, 120 great ditrigonal dodecicosidodecahedra |
| Faces | 2400 triangles, 1440 pentagons, 1440 decagrams |
| Edges | 3600+3600 |
| Vertices | 2400 |
| Vertex figure | Triangular hemiantipodium, edge lengths (1+√5)/2 (top triangle), 1 (base pseudo-triangle), and √(5–√5)/2 (sides) |
| Measures (edge length 1) | |
| Circumradius | |
| Dichoral angles | Gidditdid–3–quit gissid: 120° |
| Gidditdid–10/3–quit gissid: 108° | |
| Gidditdid–5–doe: 72° | |
| Number of external pieces | 57960 |
| Level of complexity | 184 |
| Related polytopes | |
| Army | Semi-uniform Sidpixhi |
| Regiment | Gixhidy |
| Conjugate | Small hexacosifaceted trishecatonicosachoron |
| Abstract & topological properties | |
| Euler characteristic | 120 |
| Orientable | No |
| Properties | |
| Symmetry | H4, order 14400 |
| Convex | No |
| Nature | Tame |
The great hexacosifaceted trishecatonicosachoron, or gaxifthi, is a nonconvex uniform polychoron that consists of 120 dodecahedra, 120 quasitruncated great stellated dodecahedra, and 120 great ditrigonal dodecicosidodecahedra. One dodecahedron, three quasitruncated great stellated dodecahedra, and three great ditrigonal dodecicosidodecahedra join at each vertex.
It also has 600 tetrahedra and 120 quasitruncated small stellated dodecahedra as pseudofacets.
Gallery[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the great hexacosihecatonicosidishecatonicosachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 11: Antipodiumverts" (#477).