# 33-10 step prism

33-10 step prism
File:33-10 step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells66+66+66 phyllic disphenoids
Faces132+132 scalene triangles, 66+66 isosceles triangles
Edges33+66+66+66
Vertices33
Vertex figure14-vertex polyhedron with 24 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual33-10 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(33)-10)×2R, order 132
ConvexYes
NatureTame

The 33-10 step prism is a convex isogonal polychoron, member of the step prism family. It has 198 phyllic disphenoids of three kinds as cells, with 24 cells joining at each vertex. It is also the 33-23 step prism.

The ratio between the longest and shortest edges is 1:$\sqrt{\frac{\cos\frac{\pi}{11}+5\cos\frac{\pi}{22}-3}{2\cos\frac{\pi}{11}+6\sin\frac{\pi}{22}-3}}$ ≈ 1:2.41891.

## Vertex coordinates

Coordinates for the vertices of a 33-10 step prism of circumradius 2 are given by:

• (sin(2πk/33), cos(2πk/33), sin(20πk/33), cos(20πk/33)),

where k is an integer from 0 to 32.