# 26-5 step prism

26-5 step prism
File:26-5 step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells26 tetragonal disphenoids, 52+52+52 phyllic disphenoids
Faces104+104 scalene triangles, 52+104 isosceles triangles
Edges52+52+52+52
Vertices26
Vertex figure16-vertex polyhedron with 28 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual26-5 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(26)-5)×2I, order 104
ConvexYes
NatureTame

The 26-5 step prism is a convex isogonal polychoron, member of the step prism family. It has 26 tetragonal disphenoids and 156 phyllic disphenoids of three kinds as cells. 4 tetragonal and 24 phyllic disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1:$\sqrt{\frac{2+\cos\frac{2\pi}{13}-\cos\frac{3\pi}{13}}{2-\cos\frac{\pi}{13}-\sin\frac{3\pi}{26}}}$ ≈ 1:1.78000.

## Vertex coordinates

Coordinates for the vertices of a 26-5 step prism of circumradius 2 are given by:

• (sin(πk/13), cos(πk/13), sin(5πk/13), cos(5πk/13)),

where k is an integer from 0 to 25.