Great transitional 13-5 double step prism
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| Great transitional 13-5 double step prism | |
|---|---|
| File:Great transitional 13-5 double step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Cells | 52 irregular tetrahedra, 52 phyllic disphenoids, 13 tetragonal disphenoids, 26 bilaterally-symmetric notches |
| Faces | 52+52+52+52+52 scalene triangles, 52 isosceles triangles |
| Edges | 13+26+52+52+52 |
| Vertices | 26 |
| Vertex figure | 15-vertex polyhedron with 3 tetragons and 20 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Great transitional 13-5 bigyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | S2(I2(13)-5)×2I, order 52 |
| Convex | Yes |
| Nature | Tame |
The great transitional 13-5 double step prism is a convex isogonal polychoron that consists of 26 bilaterally-symmetric notches, 13 tetragonal disphenoids, 52 phyllic disphenoids, and 52 irregular tetrahedra. 5 bilaterally-symmetric notches, 2 tetragonal disphenoids, 8 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.
The ratio between the longest and shortest edges is approximately 1:2.98928.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a great transitional 13-5 double step prism are given by:
- (a*sin(2πk/13), a*cos(2πk/13), b*sin(10πk/13), b*cos(10πk/13)),
- (b*sin(2πk/13), b*cos(2πk/13), a*sin(10πk/13), a*cos(10πk/13)),
where a ≈ 0.1342686996111878133300549, b ≈ 2.0223594019664291689707605 and k is an integer from 0 to 12.