Small transitional 13-5 double step prism
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|Small transitional 13-5 double step prism|
|File:Small transitional 13-5 double step prism.png|
|Cells||13 tetragonal disphenoids, 26 bilaterally-symmetric octahedra|
|Faces||52 scalene triangles, 26+52 isosceles triangles|
|Vertex figure||9-vertex polyhedron with 6 tetragons and 2 triangles|
|Measures (edge length 1)|
|Dual||Small transitional 13-5 bigyrochoron|
|Abstract & topological properties|
|Symmetry||S2(I2(13)-5)×2I, order 52|
The small transitional 13-5 double step prism is a convex isogonal polychoron that consists of 26 bilaterally-symmetric octahedra and 13 tetragonal disphenoids. 6 bilaterally-symmetric octahedra and 2 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.
The ratio between the longest and shortest edges is 1:a ≈ 1:2.15664, where a is the largest real root of a6-7a4+12a2-5.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a small transitional 13-5 double step prism are given by:
- (a*sin(2πk/13), a*cos(2πk/13), b*sin(10πk/13), b*cos(10πk/13)),
- (b*sin(2πk/13), b*cos(2πk/13), a*sin(10πk/13), a*cos(10πk/13)),
where a = 1/(√2(sin(5π/26)csc(π/26)-1)), b = sin(5π/26)/(√2(sin(5π/26)-sin(π/26))) and k is an integer from 0 to 12.