Small transitional 13-5 double step prism
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| Small transitional 13-5 double step prism | |
|---|---|
| File:Small transitional 13-5 double step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 13 tetragonal disphenoids, 26 bilaterally-symmetric octahedra |
| Faces | 52 scalene triangles, 26+52 isosceles triangles |
| Edges | 13+26+26+52 |
| Vertices | 26 |
| Vertex figure | 9-vertex polyhedron with 6 tetragons and 2 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Small 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 small transitional 13-5 double step prism is a convex isogonal polychoron that consists of 26 bilaterally-symmetric octahedra and 13 tetragonal disphenoids. 6 bilaterally-symmetric octahedra and 2 tetragonal disphenoids 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 1:a ≈ 1:2.15664, where a is the largest real root of a6-7a4+12a2-5.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a small 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 = 1/(√2(sin(5π/26)csc(π/26)-1)), b = sin(5π/26)/(√2(sin(5π/26)-sin(π/26))) and k is an integer from 0 to 12.