# Transitional 10-3 double step prism

Transitional 10-3 double step prism
File:Transitional 10-3 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells40 phyllic disphenoids, 20 rhombic disphenoids, 10 digonal scalenohedra
Faces40+40+40+40 scalene triangles
Edges10+20+40+40
Vertices20
Vertex figurePolyhedron with 3 tetraogns and 12 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualTransitional 10-3 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(10)-3)×2I, order 40
ConvexYes
NatureTame

The transitional 10-3 double step prism is a convex isogonal polychoron that consists of 10 digonal scalenohedra, 20 rhombic disphenoids, and 40 phyllic disphenoids. 3 digonal scalenohedra, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 10-3 step prisms.

The ratio between the longest and shortest edges is 1:$\sqrt5$ ≈ 1:2.23607.

## Vertex coordinates

Coordinates for the vertices of a transitional 10-3 double step prism are given by:

• (a*sin(2πk/10), a*cos(2πk/10), b*sin(6πk/10), b*cos(6πk/10)),
• (b*sin(2πk/10), b*cos(2πk/10), a*sin(6πk/10), a*cos(6πk/10)),

where a = 42-185/6, b = 42+185/6 and k is an integer from 0 to 9.