33-10 step prism

33-10 step prism
File:33-10 step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	66+66+66 phyllic disphenoids
Faces	132+132 scalene triangles, 66+66 isosceles triangles
Edges	33+66+66+66
Vertices	33
Vertex figure	14-vertex polyhedron with 24 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	33-10 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(33)-10)×2R, order 132
Convex	Yes
Nature	Tame

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.