# Small transitional 30-11 double gyrostep prism

Small transitional 30-11 double gyrostep prism
File:Small transitional 30-11 double gyrostep prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells60 tetrahedra, 60 skew rectangular tegums
Faces60+120 isosceles triangles, 60+120 triangles
Edges60+60+60+120
Vertices60
Vertex figurePolyhedron with 4 tetragons and 6 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualSmall transitional 30-11 antibigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(30)-11)×2I, order 120
ConvexYes
NatureTame

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:$\frac{1+\sqrt5}{2}$ ≈ 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\sqrt5-60\sqrt{1950+870\sqrt5}}}{60},\ b=\frac{\sqrt{675+225\sqrt5+15\sqrt{1950+870\sqrt5}}}{30},\$ and k is an integer from 0 to 29.