35-6 step prism

35-6 step prism
File:35-6 step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	70+70+70+70 phyllic disphenoids
Faces	140+140+140 scalene triangles, 70+70 isosceles triangles
Edges	35+70+70+70+70
Vertices	35
Vertex figure	18-vertex polyhedron with 32 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	35-6 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(35)-6)×2R, order 140
Convex	Yes
Nature	Tame

The 35-6 step prism is a convex isogonal polychoron, member of the step prism family. It has 280 phyllic disphenoids of four kinds as cells. 32 disphenoids join at each vertex. It is also the 35-29 step prism.

The ratio between the longest and shortest edges is 1:$\sqrt{\frac{4+2\cos\frac{\pi}{35}-2\cos\frac{6\pi}{35}}{4-2\cos\frac{2\pi}{35}-2\sin\frac{11\pi}{70}}}$ ≈ 1:1.98552.

Vertex coordinates

Coordinates for the vertices of a 35-6 step prism of circumradius √2 are given by:

• (sin(2πk/35), cos(2πk/35), sin(12πk/35), cos(12πk/35)),

where k is an integer from 0 to 34.