# Great 12-5 double step prism

Great 12-5 double step prism
File:Great 12-5 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells12 tetragonal disphenoids, 12+12 rhombic disphenoids, 24 phyllic disphenoids, 48+48 irregular tetrahedra
Faces24 isosceles triangles, 48+48+48+48+48+48 scalene triangles
Edges12+24+24+24+24+24+48
Vertices24
Vertex figure15-vertex polyhedron with 26 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
DualGreat 12-5 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)+×4×I, order 48
ConvexYes
NatureTame

The great 12-5 double step prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids, and 96 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 rhombic disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (a/b = 33+127/3) would yield a small 12-5 double step prism instead.

## Vertex coordinates

Coordinates for the vertices of a great 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/b is greater than 7-43 but less than 2-3 and k is an integer from 0 to 11.