# Small 13-5 double step prism

Small 13-5 double step prism
File:Small 13-5 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells52 irregular tetrahedra, 26+26 phyllic disphenoids, 13 tetragonal disphenoids
Faces52+52+52 scalene triangles, 26+52 isosceles triangles
Edges13+26+26+26+52
Vertices26
Vertex figureBilaterally-symmetric octakis digonal-octagonal gyrowedge
Measures (edge length 1)
Central density1
Related polytopes
DualSmall 13-5 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(13)-5)×2I, order 52
ConvexYes
NatureTame

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.