# 41-9 step prism

41-9 step prism
File:41-9 step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells82+82+82 phyllic disphenoids, 41 tetragonal disphenoids
Faces164+164 scalene triangles, 82+164 isosceles triangles
Edges82+82+82+82
Vertices41
Vertex figure16-vertex polyhedron with 28 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual41-9 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(37)-6)×2I, order 164
ConvexYes
NatureTame

The 41-9 step prism is a convex isogonal polychoron, member of the step prism family. It has 41 tetragonal disphenoids and 246 phyllic disphenoids of three kinds as cells. 4 tetragonal and 24 phyllic disphenoids join at each vertex. It is also the 41-32 step prism.

The ratio between the longest and shortest edges is 1:$\sqrt{\frac{4-2\cos\frac{4\pi}{41}+2\cos\frac{5\pi}{41}}{4-2\cos\frac{8\pi}{41}-2\cos\frac{10\pi}{41}}}$ ≈ 1:2.06812.

## Vertex coordinates

Coordinates for the vertices of a 41-9 step prism of circumradius 2 are given by:

• (sin(2πk/41), cos(2πk/41), sin(18πk/41), cos(18πk/41)),

where k is an integer from 0 to 40.