48-7 step prism
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| 48-7 step prism | |
|---|---|
| File:48-7 step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Cells | 96+96+96+96+96 phyllic disphenoids |
| Faces | 192+192+192+192 scalene triangles, 96+96 isosceles triangles |
| Edges | 48+96+96+96+96+96 |
| Vertices | 48 |
| Vertex figure | 22-vertex polyhedron with 40 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | 48-7 gyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | S2(I2(48)-7)×2R, order 192 |
| Convex | Yes |
| Nature | Tame |
The 48-7 step prism is a convex isogonal polychoron, member of the step prism family. It has 480 phyllic disphenoids of five kinds as cells. 40 disphenoids join at each vertex.
The ratio between the longest and shortest edges is 1: ≈ 1:2.23664.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 48-7 step prism of circumradius √2 are given by:
- (sin(πk/24), cos(πk/24), sin(7πk/24), cos(7πk/24)),
where k is an integer from 0 to 47.