50-7 step prism

50-7 step prism
File:50-7 step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	100+100+100+100+100 phyllic disphenoids, 50 tetragonal disphenoids
Faces	200+200+200+200 scalene triangles, 100+200 isosceles triangles
Edges	100+100+100+100+100+100
Vertices	50
Vertex figure	24-vertex polyhedron with 44 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	50-7 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(50)-7)×2I, order 200
Convex	Yes
Nature	Tame

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:$\sqrt{\frac{2+\cos\frac{3\pi}{25}-2\cos\frac{4\pi}{25}}{2-\cos\frac{\pi}{25}-\sin\frac{11\pi}{50}}}$ ≈ 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.