# Great transitional 12-5 double step prism

Great transitional 12-5 double step prism
File:Great transitional 12-5 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells24+48 phyllic disphenoids, 12+12 rhombic disphenoids, 12 chiral digonal scalenohedra
Faces48+48+48+48+48 scalene triangles
Edges12+24+24+24+24+48
Vertices24
Vertex figure13-vertex polyhedron with 3 tetragons and 16 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualGreat transitional 12-5 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(12)-5)×2R, order 48
ConvexYes
NatureTame

The great transitional 12-5 double step prism is a convex isogonal polychoron that consists of 12 chiral digonal scalenohedra, 24 rhombic disphenoids of two kinds, and 72 phyllic disphenoids of two kinds. 3 digonal scalenohedra, 4 rhombic disphenoids, and 12 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

The ratio between the longest and shortest edges is 1:${\displaystyle \frac{\sqrt{30}}{2}}$ ≈ 1:2.73861.

## Vertex coordinates

Coordinates for the vertices of a great transitional 12-5 double step prism are given by:

• (a*sin(2πk/12), a*cos(2πk/12), b*sin(10πk/12), b*cos(10πk/12)),
• (b*sin(2πk/12), b*cos(2πk/12), a*sin(10πk/12), a*cos(10πk/12)),

where a = (2-3)/2, b = (2+3)/2 and k is an integer from 0 to 11.