Great transitional 12-5 double step prism

Great transitional 12-5 double step prism
File:Great transitional 12-5 double step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	24+48 phyllic disphenoids, 12+12 rhombic disphenoids, 12 chiral digonal scalenohedra
Faces	48+48+48+48+48 scalene triangles
Edges	12+24+24+24+24+48
Vertices	24
Vertex figure	13-vertex polyhedron with 3 tetragons and 16 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Great transitional 12-5 bigyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(12)-5)×2R, order 48
Convex	Yes
Nature	Tame

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:$\frac{\sqrt{30}}{2}$ ≈ 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.

External links

• Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".