Small hexacosihecatonicosihecatonicosachoron
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Small hexacosihecatonicosihecatonicosachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Sixhihy |
Coxeter diagram | o3o3/2x5x5*b () |
Elements | |
Cells | 600 tetrahedra, 120 dodecahedra, 120 small dodecicosidodecahedra |
Faces | 2400 triangles, 1440 pentagons, 720 decagons |
Edges | 3600+3600 |
Vertices | 2400 |
Vertex figure | Crossed triangular frustum, edge lengths 1 (small base), (1+√5)/2 (large base), and √(5+√5)/2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5\frac{3665+1622\sqrt5}{4} \approx 9114.87782} |
Dichoral angles | Saddid–10–saddid: 144° |
Saddid–5–doe: 144° | |
Saddid–3–tet: | |
Number of external pieces | 4560 |
Level of complexity | 12 |
Related polytopes | |
Army | Sidpixhi |
Regiment | Sidpixhi |
Conjugate | Great hexacosihecatonicosihecatonicosachoron |
Abstract & topological properties | |
Flag count | 86400 |
Euler characteristic | –1080 |
Orientable | Yes |
Properties | |
Symmetry | H_{4}, order 14400 |
Convex | No |
Nature | Tame |
The small hexacosihecatonicosihecatonicosachoron, or sixhihy, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 small dodecicosidodecahedra. 1 tetrahedron, 1 dodecahedron, and 3 small dodecicosidodecahedra join at each vertex.
Gallery[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the small disprismatohexacosihecatonicosachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 11: Antipodiumverts" (#457).
- Klitzing, Richard. "sixhihy".