13-5 step prism

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13-5 step prism
File:13-5 step prism.png
Cells26 phyllic disphenoids, 13 tetragonal disphenoids
Faces26+52 isosceles triangles
Vertex figureProdigonal antiprismatic symmetric snub disphenoid
Measures (circumradius , based on a uniform duoprism)
Edge lengths5-valence (26):
 4-valence (26):
Central density1
Related polytopes
Dual13-5 gyrochoron
Abstract & topological properties
Euler characteristic0
SymmetryS2(I2(13)-5)×2I, order 52

The 13-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 13 tetragonal disphenoids and 26 phyllic disphenoids as cells. 4 tetragonal and 8 phyllic disphenoids join at each vertex. It is also the pentagonal funk tegum.

Compared to other 13-vertex step prisms, this polychoron has doubled symmetry, because 13 is a factor of 52+1 = 26.

Its vertex figure is topologically equivalent to the Johnson solid snub disphenoid.

The ratio between the longest and shortest edges is 1: ≈ 1:1.19192.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 13-5 step prism of circumradius 2 are given by:

  • (sin(2πk/13), cos(2πk/13), sin(10πk/13), cos(10πk/13)),

where k is an integer from 0 to 12.

Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

External links[edit | edit source]