# Small transitional 13-5 double step prism

Small transitional 13-5 double step prism
File:Small transitional 13-5 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells13 tetragonal disphenoids, 26 bilaterally-symmetric octahedra
Faces52 scalene triangles, 26+52 isosceles triangles
Edges13+26+26+52
Vertices26
Vertex figure9-vertex polyhedron with 6 tetragons and 2 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualSmall transitional 13-5 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(13)-5)×2I, order 52
ConvexYes
NatureTame

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

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.