Transitional 12-5 double gyrostep prism

Transitional 12-5 double gyrostep prism
File:Transitional 12-5 double gyrostep prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	24 phyllic disphenoids, 24 tetragonal disphenoids, 24 tetragonal antiwedges
Faces	48 scalene triangles, 48+48 isosceles triangles, 24 kites
Edges	24+24+24+48
Vertices	24
Vertex figure	Polyhedron with 2 tetragons and 12 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Transitional 12-5 antibigyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(12)-5)×2I, order 48
Convex	Yes
Nature	Tame

The transitional 12-5 double gyrostep prism is a convex isogonal polychoron that consists of 24 tetragonal antiwedges, 24 tetragonal disphenoids, and 24 phyllic disphenoids. 6 tetragonal antiwedges, 4 tetragonal disphenoids, and 4 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:$\sqrt{4+2\sqrt2}$ ≈ 1:2.61313.

Vertex coordinates

Coordinates for the vertices of a transitional 12-5 double gyrostep 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 = √36-6√18-12√2/12, b = √36+6√18-12√2/12 and k is an integer from 0 to 11.

External links

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