# 15-4 step prism

15-4 step prism
File:15-4 step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells30+30 phyllic disphenoids
Faces60 scalene triangles, 30+30 isosceles triangles
Edges15+30+30
Vertices15
Vertex figureParatetraaugmented digonal scalenohedron
Measures (circumradius $\sqrt2$ , based on a uniform duoprism)
Edge lengths6-valence (30): $\sqrt{\frac{7-\sqrt5}{2}} ≈ 1.54336$ 6-valence (15): $\sqrt{5-\sqrt5} ≈ 1.66251$ 3-valence (30): $\sqrt{\frac{7+\sqrt5}{2}} ≈ 2.14896$ Central density1
Related polytopes
Dual15-4 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(15)-4)×2R, order 60
ConvexYes
NatureTame

The 15-4 step prism is a convex isogonal polychoron and a member of the step prism family. It has 60 phyllic disphenoids of two kinds as cells, with 16 joining at each vertex.

Compared to other 15-vertex step prisms, this polychoron has doubled symmetry, because 15 is a factor of 42-1 = 15.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{594+154\sqrt5}}{22}$ ≈ 1:1.39239.

## Vertex coordinates

Coordinates for the vertices of a 15-4 step prism of circumradius 2 are given by:

• (sin(2πk/15), cos(2πk/15), sin(8πk/15), cos(8πk/15)),

where k is an integer from 0 to 14.