# 10-2 double step prism

10-2 double step prism
File:10-2 double step prism.png
Rank4
TypeIsogonal
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): ${\displaystyle {\frac {\sqrt {4-{\sqrt {5}}}}{2}}\approx 0.66407}$
4-valence (40): ${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
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:${\displaystyle {\frac {\sqrt {176+44{\sqrt {5}}}}{11}}}$ \approx 1:1.50588.

## Vertex coordinates

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

• ${\displaystyle (a\sin(2\pi k/10),a\cos(2\pi k/10),a\sin(6\pi k/10),a\cos(6\pi k/10))}$,
• ${\displaystyle (a\sin(2\pi k/10),a\cos(2\pi k/10),-a\sin(6\pi k/10),-a\cos(6\pi k/10))}$,

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