37-6 step prism
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|37-6 step prism|
|File:37-6 step prism.png|
|Cells||37 tetragonal disphenoids, 74+74+74+74 phyllic disphenoids|
|Faces||148+148+148 scalene triangles, 74+148 isosceles triangles|
|Vertex figure||20-vertex polyhedron with 36 triangular faces|
|Measures (edge length 1)|
|Abstract & topological properties|
|Symmetry||S2(I2(37)-6)×2I, order 148|
The 37-6 step prism is a convex isogonal polychoron, member of the step prism family. It has 37 tetragonal disphenoids and 296 phyllic disphenoids of four kinds as cells. 4 tetragonal and 32 phyllic disphenoids join at each vertex. It is also the 37-31 step prism.
The ratio between the longest and shortest edges is 1: ≈ 1:2.08153.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 37-6 step prism of circumradius √2 are given by:
- (sin(2πk/37), cos(2πk/37), sin(12πk/37), cos(12πk/37)),
where k is an integer from 0 to 36.