# Transitional 12-5 double gyrostep prism

Transitional 12-5 double gyrostep prism
File:Transitional 12-5 double gyrostep prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells24 phyllic disphenoids, 24 tetragonal disphenoids, 24 tetragonal antiwedges
Faces48 scalene triangles, 48+48 isosceles triangles, 24 kites
Edges24+24+24+48
Vertices24
Vertex figurePolyhedron with 2 tetragons and 12 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualTransitional 12-5 antibigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(12)-5)×2I, order 48
ConvexYes
NatureTame

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 = 36-618-122/12, b = 36+618-122/12 and k is an integer from 0 to 11.