30-11 step prism

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30-11 step prism
File:30-11 step prism.png
Rank4
TypeIsogonal
Elements
Cells60+60 phyllic disphenoids, 30 rhombic disphenoids
Faces120+120 scalene triangles, 60 isosceles triangles
Edges30+30+60+60
Vertices30
Vertex figure12-vetex polyhedron with 20 triangular faces
Measures (circumradius , based on a uniform duoprism)
Edge lengths8-valence (30):
 4-valence (30):
 5-valence (60):
 4-valence (60):
Central density1
Related polytopes
Dual30-11 gyrochoron
Abstract & topological properties
Flag count3600
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(30)-11)×2R, order 120
ConvexYes
NatureTame

The 30-11 step prism is a convex isogonal polychoron, member of the step prism family. It has 30 rhombic disphenoids and 120 phyllic disphenoids of two kinds as cells. It is also the 30-19 step prism.

The ratio between the longest and shortest edges is 1: ≈ 1:2.10406.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 30-11 step prism of circumradius 2 are given by:

  • ,

where k is an integer from 0 to 29.