Small transitional 30-11 double gyrostep prism

Small transitional 30-11 double gyrostep prism
File:Small transitional 30-11 double gyrostep prism.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	60 tetrahedra, 60 skew rectangular tegums
Faces	60+120 isosceles triangles, 60+120 triangles
Edges	60+60+60+120
Vertices	60
Vertex figure	Polyhedron with 4 tetragons and 6 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Small transitional 30-11 antibigyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(30)-11)×2I, order 120
Convex	Yes
Nature	Tame

The small transitional 30-11 double gyrostep prism is a convex isogonal polychoron that consists of 60 skew rectangular tegums and 60 tetrahedra. 6 skew rectangular tegums and 4 tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 30-11 step prisms.

It can also be obtained as a diminishing of the hexacosichoron and is also a vertex-faceting of the grand antiprism.

The ratio between the longest and shortest edges is 1:${\frac {1+{\sqrt {5}}}{2}}$ ≈ 1:1.61803.

Vertex coordinates

Coordinates for the vertices of a small transitional 30-11 double gyrostep prism are given by:

• (a*sin(πk/15), a*cos(πk/15), b*sin(11πk/15), b*cos(11πk/15)),
• (b*sin(πk/15), b*cos(πk/15), -a*sin(11πk/15), -a*cos(11πk/15)),

where $a={\frac {\sqrt {2700+900{\sqrt {5}}-60{\sqrt {1950+870{\sqrt {5}}}}}}{60}},\ b={\frac {\sqrt {675+225{\sqrt {5}}+15{\sqrt {1950+870{\sqrt {5}}}}}}{30}},\$ and k is an integer from 0 to 29.