# 39-14 step prism

39-14 step prism
File:39-14 step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells78+78+78 phyllic disphenoids
Faces156+156 scalene triangles, 78+78 isosceles triangles
Edges39+78+78+78
Vertices39
Vertex figure14-vertex polyhedron with 24 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual39-14 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(39)-14)×2R, order 156
ConvexYes
NatureTame

The 39-14 step prism is a convex isogonal polychoron, member of the step prism family. It has 234 phyllic disphenoids of three kinds as cells. 24 disphenoids join at each vertex. It is also the 39-25 step prism.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{2-\cos\frac{2\pi}{39}+\sin\frac{17\pi}{78}}}{2\sin\frac{\pi}{13}}$ ≈ 1:2.67999.

## Vertex coordinates

Coordinates for the vertices of a 39-14 step prism of circumradius 2 are given by:

• (sin(2πk/39), cos(2πk/39), sin(28πk/39), cos(28πk/39)),

where k is an integer from 0 to 38.