Small 13-5 double step prism

Small 13-5 double step prism
File:Small 13-5 double step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	52 irregular tetrahedra, 26+26 phyllic disphenoids, 13 tetragonal disphenoids
Faces	52+52+52 scalene triangles, 26+52 isosceles triangles
Edges	13+26+26+26+52
Vertices	26
Vertex figure	Bilaterally-symmetric octakis digonal-octagonal gyrowedge
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Small 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 13-5 double step prism is a convex isogonal polychoron that consists of 13 tetragonal disphenoids, 52 phyllic disphenoids of two kinds and 52 irregular tetrahedra obtained as the convex hull of two orthogonal 13-5 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.58440.

Vertex coordinates

Coordinates for the vertices of a small 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 = √2/(2sec(2π/13)+sec(2π/13)√4+2cos(π/13)+2sin(3π/26)-2), b = (√2+√2+cos(π/13)+sin(3π/26))/(2-2cos(2π/13)+√4+2cos(π/13)+2sin(3π/26)) and k is an integer from 0 to 12.