17-5 step prism

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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 , based on a uniform duoprism)
Edge lengths7-valence (17):
 6-valence (17):
 4-valence (17):
 4-valence (17):
 3-valence (17):
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[edit | edit source]

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: ≈ 1:0.94418.

External links[edit | edit source]