40-11 step prism

From Polytope Wiki
Jump to navigation Jump to search
40-11 step prism
File:40-11 step prism.png
Rank4
TypeIsogonal
Elements
Cells80+80+80 phyllic disphenoids
Faces160+160 scalene triangles, 80+80 isosceles triangles
Edges40+80+80+80
Vertices40
Vertex figure14-vertex polyhedron with 24 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual40-11 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(40)-11)×2R, order 160
ConvexYes
NatureTame

The 40-11 step prism is a convex isogonal polychoron, member of the step prism family. It has 240 phyllic disphenoids of three kinds as cells. 24 disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1: ≈ 1:2.28825.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 40-11 step prism of circumradius 2 are given by:

  • (sin(πk/20), cos(πk/20), sin(11πk/20), cos(11πk/20)),

where k is an integer from 0 to 39.