40-9 step prism

40-9 step prism
(OFF file)
Rank	4
Type	Isogonal
Elements
Cells	80+80+80 phyllic disphenoids, 40 rhombic disphenoids
Faces	160+160+160 scalene triangles, 80 isosceles triangles
Edges	40+40+80+80+80
Vertices	40
Vertex figure	16-vertex polyhedron with 28 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	40-9 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(40)-9)×2R, order 160
Convex	Yes
Nature	Tame

The 40-9 step prism, also known as the digonal double pentaswirlprism, is a convex isogonal polychoron, member of the step prism family. It has 40 rhombic disphenoids and 240 phyllic disphenoids of three kinds as cells. 4 rhombic and 24 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal digonal prismatic swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {3+{\sqrt {5}}}}$ ≈ 1:2.28825.

Vertex coordinates

Coordinates for the vertices of a 40-9 step prism of circumradius √2 are given by:

• (sin(πk/20), cos(πk/20), sin(9πk/20), cos(9πk/20)),

where k is an integer from 0 to 39.