# Small transitional 12-5 double step prism

Small transitional 12-5 double step prism
File:Small transitional 12-5 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells12 tetragonal disphenoids, 12 rectangular gyroprisms
Faces24+48 isosceles triangles, 12 rectangles
Edges12+24+24+24
Vertices24
Vertex figureDigonal-rectangular gyronotch
Measures (edge length 1)
Central density1
Related polytopes
DualSmall transitional 12-5 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(12)-5)×2R, order 48
ConvexYes
NatureTame

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.