Hexacosichoric prism
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Hexacosichoric prism | |
---|---|
File:Hexacosichoric prism.png | |
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Exip |
Coxeter diagram | x o5o3o3x () |
Elements | |
Tera | 600 tetrahedral prisms, 2 hexacosichora |
Cells | 1200 tetrahedra, 1200 triangular prisms |
Faces | 2400 triangles, 720 squares |
Edges | 120+1440 |
Vertices | 240 |
Vertex figure | Icosahedral pyramid, edge lengths 1 (base), √2 (legs) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tepe–trip–tepe: |
Ex–tet–tepe: 90° | |
Height | 1 |
Central density | 1 |
Number of external pieces | 602 |
Level of complexity | 5 |
Related polytopes | |
Army | Exip |
Regiment | Exip |
Dual | Hecatonicosachoric tegum |
Conjugate | Grand hexacosichoric prism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H4×A1, order 28800 |
Convex | Yes |
Nature | Tame |
The hexacosichoric prism or exip is a prismatic uniform polyteron that consists of 2 hexacosichora and 600 tetrahedral prisms. 1 hexacosichoron and 20 tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the hexacosichoron, which also makes it a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a hexacosichoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:
together with all the even permutations of the first four coordinates of:
External links[edit | edit source]
- Klitzing, Richard. "Exip".