# 50-7 step prism

50-7 step prism
File:50-7 step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells100+100+100+100+100 phyllic disphenoids, 50 tetragonal disphenoids
Faces200+200+200+200 scalene triangles, 100+200 isosceles triangles
Edges100+100+100+100+100+100
Vertices50
Vertex figure24-vertex polyhedron with 44 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual50-7 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(50)-7)×2I, order 200
ConvexYes
NatureTame

The 50-7 step prism is a convex isogonal polychoron, member of the step prism family. It has 50 tetragonal disphenoids and 500 phyllic disphenoids of five kinds as cells. 4 tetragonal and 40 phyllic disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1:${\displaystyle \sqrt{\frac{2+\cos\frac{3\pi}{25}-2\cos\frac{4\pi}{25}}{2-\cos\frac{\pi}{25}-\sin\frac{11\pi}{50}}}}$ ≈ 1:2.35436.

## Vertex coordinates

Coordinates for the vertices of a 50-7 step prism of circumradius 2 are given by:

• (sin(πk/25), cos(πk/25), sin(7πk/25), cos(7πk/25)),

where k is an integer from 0 to 49.