19-7 step prism

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19-7 step prism
Rank4
TypeIsogonal
Elements
Cells19+19+19+19 phyllic disphenoids
Faces38+38+38 scalene triangles, 19+19 isosceles triangles
Edges19+19+19+19+19
Vertices19
Vertex figureEdge-expanded heptagonal tegum
Measures (circumradius , based on a uniform duoprism)
Edge lengths7-valence (19):
 5-valence (19):
 4-valence (19):
 4-valence (19):
 4-valence (19):
Central density1
Related polytopes
Dual19-7 gyrochoron
Abstract & topological properties
Flag count1824
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(19)-7), order 38
ConvexYes
NatureTame

The 19-7 step prism is a convex isogonal polychoron and a member of the step prism family. It has 76 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 19-8 step prism. It is also the heptagonal funk tegum.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.67674.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 19-7 step prism inscribed in an enneadecagonal duoprism with base lengths a and b are given by:

  • ,

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: ≈ 1:1.06046.

External links[edit | edit source]