# 17-5 step prism

17-5 step prism
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryI2(17)+×2×I, order 34
Elements
Vertex figure10-vertex polyhedron with 16 triangular faces
Cells17+17+17+17 phyllic disphenoids
Faces17+17+34+34+34 scalene triangles
Edges17+17+17+17+17
Vertices17
Measures (circumradius ${\displaystyle \sqrt2}$, based on a uniform duoprism)
Edge lengths7-valence (17): ${\displaystyle 2\sqrt{\sin^2\frac{2\pi}{17}+\sin^2\frac{3\pi}{17}} ≈ 1.27691}$
6-valence (17): ${\displaystyle 2\sqrt{\sin^2\frac{\pi}{17}+\cos^2\frac{7\pi}{34}} ≈ 1.63780}$
4-valence (17): ${\displaystyle 2\sqrt{\sin^2\frac{\pi}{17}+\sin^2\frac{4\pi}{17}} ≈ 1.70997}$
4-valence (17): ${\displaystyle 2\sqrt{\sin^2\frac{\pi}{17}+\cos^2\frac{3\pi}{34}} ≈ 1.95844}$
3-valence (17): ${\displaystyle \sqrt{4-2\cos\frac{4\pi}{17}+2\cos\frac{3\pi}{17}} ≈ 2.05485}$
Central density1
Euler characteristic0
Related polytopes
Dual17-5 gyrochoron
Properties
ConvexYes
OrientableYes
NatureTame

The 17-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 68 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 17-7 step prism.

## Vertex coordinates

Coordinates for the vertices of a 17-5 step prism inscribed in a heptadecagonal duoprism with base lengths a and b are given by:

• (a*sin(2πk/17), a*cos(2πk/17), b*sin(10πk/17), b*cos(10πk/17)),

where k is an integer from 0 to 16. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:${\displaystyle \sqrt{\frac{\cos\frac{3\pi}{17}+\cos\frac{4\pi}{17}}{\cos\frac{2\pi}{17}+\cos\frac{3\pi}{17}}}}$ ≈ 1:0.94418.