Medial 13-5 double step prism
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| Medial 13-5 double step prism | |
|---|---|
| File:Medial 13-5 double step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Cells | 13 tetragonal disphenoids, 26 phyllic disphenoids, 52+52 irregular tetrahedra |
| Faces | 26+52 isosceles triangles, 52+52+52+52 scalene triangles |
| Edges | 13+26+26+52+52 |
| Vertices | 26 |
| Vertex figure | 13-vertex polyhedron with 22 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Medial 13-5 bigyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | I2(13)+×4×I, order 52 |
| Convex | Yes |
| Nature | Tame |
The medial 13-5 double step prism is a convex isogonal polychoron that consists of 13 tetragonal disphenoids, 26 phyllic disphenoids, and 104 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.
This polychoron cannot be optimized using the ratio method, because the solution (a/b = (2+√4+2cos(π/13)+2sin(3π/26))/(2cos(2π/13)) would yield a small 13-5 double step prism instead.