13-2 step prism

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13-2 step prism
Rank4
TypeIsogonal
Elements
Cells13+13+13+13+13 phyllic disphenoids
Faces26+26+26+26 scalene triangles, 13+13 isosceles triangles
Edges13+13+13+13+13+13
Vertices13
Vertex figureRidge-tritriakis bi-apiculated tetrahedron
Measures (circumradius , based on a uniform duoprism)
Edge lengths11-valence (13):
 3-valence (13):
 4-valence (13):
 4-valence (13):
 4-valence (13):
 4-valence (13):
Central density1
Related polytopes
Dual13-2 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(13)-2), order 26
ConvexYes
NatureTame

The 13-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 65 phyllic disphenoids of five kinds as cells, with 20 joining at each vertex. It can also be constructed as the 13-6 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.16752.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 13-2 step prism inscribed in a tridecagonal duoprism with base lengths a and b are given by:

  • (a*sin(2πk/13), a*cos(2πk/13), b*sin(4πk/13), b*cos(4πk/13)),

where k is an integer from 0 to 12. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to : ≈ 1:2.41846.

External links[edit | edit source]