48-17 step prism
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| 48-17 step prism | |
|---|---|
| File:48-17 step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Cells | 96+96+96 phyllic disphenoids, 48 rhombic disphenoids |
| Faces | 192+192+192 scalene triangles, 96 isosceles triangles |
| Edges | 48+48+96+96+96 |
| Vertices | 48 |
| Vertex figure | 16-vertex polyhedron with 28 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | 48-17 gyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | S2(I2(48)-17)×2R, order 192 |
| Convex | Yes |
| Nature | Tame |
The 48-17 step prism is a convex isogonal polychoron, member of the step prism family. It has 48 rhombic disphenoids and 288 phyllic disphenoids of three kinds as cells. 4 rhombic and 24 phyllic disphenoids join at each vertex.
The ratio between the longest and shortest edges is 1: ≈ 1:3.25936.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 48-17 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.