# 10-2 double step prism

10-2 double step prism
File:10-2 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells40 phyllic disphenoids, 20 rhombic disphenoids, 20 tetragonal disphenoids
Faces80 scalene triangles, 80 isosceles triangles
Edges20+40+40
Vertices20
Vertex figureTetrakis parallelogramic alterprism
Measures (longest edge length 1)
Edge lengths6-valence (40): ${\displaystyle \frac{\sqrt{4-\sqrt5}}{2} ≈ 0.66407}$
4-valence (40): ${\displaystyle \frac{\sqrt3}{2} ≈ 0.86603}$
4-valence (20): 1
Central density1
Related polytopes
Dual10-2 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(10)×2-2)×2I, order 80
ConvexYes
NatureTame

The 10-2 double step prism is a convex isogonal polychoron that consists of 20 tetragonal disphenoids, 20 rhombic disphenoids, and 40 phyllic disphenoids. 4 tetragonal disphenoids, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two opposite 10-2 step prisms.

The ratio between the longest and shortest edges is 1:${\displaystyle \frac{\sqrt{176+44\sqrt5}}{11}}$ ≈ 1:1.50588.

## Vertex coordinates

Coordinates for the vertices of a 10-2 double step prism are given by:

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

where a = 1/2 and k is an integer from 0 to 9.