17-4 step prism

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17-4 step prism
File:17-4 step prism.png
Rank4
TypeIsogonal
Elements
Cells34+34 phyllic disphenoids, 17 tetragonal disphenoids
Faces68 scalene triangles, 34+68 isosceles triangles
Edges34+34+34
Vertices17
Vertex figureParatetraaugmented triakis tetragonal disphenoid
Measures (circumradius , based on a uniform duoprism)
Edge lengths8-valence (34):
 4-valence (34):
 3-valence (34):
Central density1
Related polytopes
Dual17-4 gyrochoron
Abstract & topological properties
Flag count2040
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(17)-4)×2I, order 68
ConvexYes
NatureTame

The 17-4 step prism is a convex isogonal polychoron, member of the step prism family. It has 17 tetragonal disphenoids and 68 phyllic disphenoids of two kinds as cells. 2 tetragonal and 16 phyllic disphenoids join at each vertex.

Compared to other 17-vertex step prisms, this polychoron has doubled symmetry, because 17 is a factor of 42+1 = 17.

The ratio between the longest and shortest edges is 1: ≈ 1:1.51687.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 17-4 step prism of circumradius 2 are given by:

  • ,

where k is an integer from 0 to 16.

External links[edit | edit source]