21-8 step prism
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|21-8 step prism|
|File:21-8 step prism.png|
|Cells||42+42 phyllic disphenoids|
|Faces||84 scalene triangles, 42+42 isosceles triangles|
|Vertex figure||10-vertex polyhedron with 16 triangular faces|
|Measures (edge length 1)|
|Edge lengths||6-valence (21):|
|Abstract & topological properties|
|Symmetry||S2(I2(21)-8)×2R, order 84|
The 21-8 step prism is a convex isogonal polychoron, member of the step prism family. It has 84 phyllic disphenoids of two kinds as cells, with 16 joining at each vertex..
The ratio between the longest and shortest edges is 1: ≈ 1:1.53638.
Compared to other 21-vertex step prisms, this polychoron has doubled symmetry, because 21 is a factor of 82-1 = 63.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 21-8 step prism of circumradius √2 are given by:
- (sin(2πk/21), cos(2πk/21), sin(16πk/21), cos(15πk/21)),
where k is an integer from 0 to 20.