19-3 step prism

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19-3 step prism
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryI2(19)+×2×I, order 38
Elements
Vertex figure14-vertex polyhedron with 24 triangular faces
Cells19+19+19+19+19+19 phyllic disphenoids
Faces19+19+38+38+38+38+38 scalene triangles
Edges19+19+19+19+19+19+19
Vertices19
Measures (circumradius , based on a uniform duoprism)
Edge lengths12-valence (19):
 6-valence (19):
 3-valence (19):
 4-valence (19):
 4-valence (19):
 4-valence (19):
 4-valence (19):
Central density1
Euler characteristic0
Related polytopes
Dual19-3 gyrochoron
Properties
ConvexYes
OrientableYes
NatureTame

The 19-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 114 phyllic disphenoids of six kinds as cells, with 24 joining at each vertex. It can also be constructed as the 19-6 step prism.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 19-3 step prism inscribed in an enneadecagonal duoprism with base lengths a and b are given by:

  • (a*sin(2πk/19), a*cos(2πk/19), b*sin(6πk/19), b*cos(6πk/19)),

where k is an integer from 0 to 18. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:1.83802.

External links[edit | edit source]