Small tritrigonary hexacositrishecatonicosachoron
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Small tritrigonary hexacositrishecatonicosachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Stut xethi |
Coxeter diagram | x3o3/2o3/2x5*a5*c |
Elements | |
Cells | 600 tetrahedra, 120 great ditrigonary icosidodecahedra, 120 truncated dodecahedra, 120 small dodecicosidodecahedra |
Faces | 2400+2400 triangles, 1440 pentagons, 1440 decagons |
Edges | 3600+7200 |
Vertices | 2400 |
Vertex figure | Crossed retrotriangular cupola, edge lengths 1 (top triangle and 3 edges of base tripod), (1+√5)/2 (remaining base edges), and √(5+√5)/2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Gidtid–5–saddid: 144° |
Tet–3–saddid: | |
Gidtid–3–tid: 120° | |
Saddid–10–tid: 108° | |
Related polytopes | |
Army | Semi-uniform sidpixhi, edge lengths (dodecahedra), 1 (tetrahedra) |
Regiment | Stut phiddix |
Conjugate | Great tritrigonary hexacositrishecatonicosachoron |
Abstract & topological properties | |
Flag count | 144000 |
Euler characteristic | –1680 |
Orientable | Yes |
Properties | |
Symmetry | H4, order 14400 |
Convex | No |
Nature | Tame |
The small tritrigonary hexacositrishecatonicosachoron, or stut xethi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 truncated dodecahedra, 120 small dodecicosidodecahedra, and 120 great ditrigonary icosidodecahedra. 1 tetrahedron, 3 truncated dodecahedra, 3 small dodecicosidodecahedra, and 1 great ditrigonary icosidodecahedron join at each vertex.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the small tritrigonary prismatohecatonicosidishexacosichoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 24: Stut Phiddix Regiment" (#1309).
- Klitzing, Richard. "stut xethi".