Small transitional 12-5 double step prism

Small transitional 12-5 double step prism
File:Small transitional 12-5 double step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	12 tetragonal disphenoids, 12 rectangular gyroprisms
Faces	24+48 isosceles triangles, 12 rectangles
Edges	12+24+24+24
Vertices	24
Vertex figure	Digonal-rectangular gyronotch
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Small 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 small transitional 12-5 double step prism is a convex isogonal polychoron that consists of 12 rectangular gyroprisms and 12 tetragonal disphenoids. 2 rectangular gyroprisms and 4 tetragonal 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:$\sqrt3$ ≈ 1:1.73205.

Vertex coordinates

Coordinates for the vertices of a small 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 = (√3-1)/4, b = (1+√3)/4 and k is an integer from 0 to 11.

External links

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