34-13 step prism

The 34-13 step prism is a convex isogonal polychoron, member of the step prism family. It has 34 tetragonal disphenoids and 136 phyllic disphenoids of two kinds as cells. 4 tetragonal and 16 phyllic disphenoids join at each vertex. It is also the 34-21 step prism.

34-13 step prism
File:34-13 step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	68+68 phyllic disphenoids, 34 tetragonal disphenoids
Faces	136 scalene triangles, 68+136 isosceles triangles
Edges	68+68+68
Vertices	30
Vertex figure	12-vertex polyhedron with 20 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	34-13 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(34)-13)×2I, order 136
Convex	Yes
Nature	Tame

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{61408+7878\sqrt{17}+202\sqrt{22525+2704\sqrt{17}}}}{202}$ ≈ 1:1.79149.

Vertex coordinates

Coordinates for the vertices of a 34-13 step prism of circumradius √2 are given by:

• (sin(πk/17), cos(πk/17), sin(13πk/17), cos(13πk/17)),

where k is an integer from 0 to 33.