48-7 step prism

48-7 step prism
File:48-7 step prism.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	96+96+96+96+96 phyllic disphenoids
Faces	192+192+192+192 scalene triangles, 96+96 isosceles triangles
Edges	48+96+96+96+96+96
Vertices	48
Vertex figure	22-vertex polyhedron with 40 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	48-7 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(48)-7)×2R, order 192
Convex	Yes
Nature	Tame

The 48-7 step prism is a convex isogonal polychoron, member of the step prism family. It has 480 phyllic disphenoids of five kinds as cells. 40 disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1:${\frac {\sqrt {3280+984{\sqrt {2}}+82{\sqrt {1068+714{\sqrt {2}}}}}}{41}}$ ≈ 1:2.23664.

Vertex coordinates

Coordinates for the vertices of a 48-7 step prism of circumradius √2 are given by:

• (sin(πk/24), cos(πk/24), sin(7πk/24), cos(7πk/24)),

where k is an integer from 0 to 47.