18-5 step prism

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18-5 step prism
Rank4
TypeIsogonal
Elements
Cells18+18+18+18 phyllic disphenoids
Faces36+36+36 scalene triangles, 18+18 isosceles triangles
Edges18+18+18+18+18
Vertices18
Vertex figureMetabitriakis snub disphenoid
Measures (circumradius , based on a uniform duoprism)
Edge lengths6-valence (18):
 5-valence (18):
 6-valence (18):
 4-valence (18):
 3-valence (18):
Central density1
Related polytopes
Dual18-5 gyrochoron
Abstract & topological properties
Flag count1728
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(18)-5), order 36
ConvexYes
NatureTame

The 18-5 step prism, also known as the 9-2 double step prism, is a convex isogonal polychoron and a member of the step prism family. It has 72 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 18-7 step prism, or as the convex hull of two opposite 9-2 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.41421.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of an 18-5 step prism inscribed in an octadecagonal duoprism with base lengths a and b are given by:

  • ,

where k is an integer from 0 to 17. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:0.90289.

External links[edit | edit source]