# 15-2 step prism

15-2 step prism
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryI2(15)+×2×I, order 30
Elements
Cells15+15+15+15+15+15 phyllic disphenoids
Faces15+15+30+30+30+30+30 scalene triangles
Edges15+15+15+15+15+15+15
Vertices15
Measures (circumradius ${\displaystyle \sqrt2}$, based on a uniform duoprism)
Edge lengths13-valence (15): ${\displaystyle \sqrt{\frac{7-\sqrt{15+6\sqrt5}}{2}} ≈ 0.91359}$
3-valence (15): ${\displaystyle \sqrt{\frac{7-\sqrt{15-6\sqrt5}}{2}} ≈ 1.69434}$
4-valence (15): ${\displaystyle \sqrt{\frac{7+\sqrt{15-6\sqrt5}}{2}} ≈ 2.03204}$
4-valence (15+15): ${\displaystyle \sqrt5 ≈ 2.23607}$
4-valence (15): ${\displaystyle \sqrt6 ≈ 2.44949}$
4-valence (15): ${\displaystyle \sqrt{\frac{7+\sqrt{15+6\sqrt5}}{2}} ≈ 2.48301}$
Central density1
Euler characteristic0
Related polytopes
Dual15-2 gyrochoron
Properties
ConvexYes
OrientableYes
NatureTame

The 15-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 90 phyllic disphenoids of six kinds as cells, with 24 joining at each vertex. It can also be constructed as the 15-7 step prism.

## Vertex coordinates

Coordinates for the vertices of a 15-2 step prism inscribed in a pentadecagonal duoprism with base lengths a and b are given by:

• (a*sin(2πk/15), a*cos(2πk/15), b*sin(4πk/15), b*cos(4πk/15)),

where k is an integer from 0 to 14. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:${\displaystyle \frac{\sqrt{7+3\sqrt5+\sqrt{150+66\sqrt5}}}{2}}$ ≈ 1:2.78203.