Great transitional 13-5 double step prism
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|Great transitional 13-5 double step prism|
|File:Great transitional 13-5 double step prism.png|
|Cells||52 irregular tetrahedra, 52 phyllic disphenoids, 13 tetragonal disphenoids, 26 bilaterally-symmetric notches|
|Faces||52+52+52+52+52 scalene triangles, 52 isosceles triangles|
|Vertex figure||15-vertex polyhedron with 3 tetragons and 20 triangles|
|Measures (edge length 1)|
|Dual||Great transitional 13-5 bigyrochoron|
|Abstract & topological properties|
|Symmetry||S2(I2(13)-5)×2I, order 52|
The great transitional 13-5 double step prism is a convex isogonal polychoron that consists of 26 bilaterally-symmetric notches, 13 tetragonal disphenoids, 52 phyllic disphenoids, and 52 irregular tetrahedra. 5 bilaterally-symmetric notches, 2 tetragonal disphenoids, 8 phyllic disphenoids, and 8 irregular tetrahedra 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 approximately 1:2.98928.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a great 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 ≈ 0.1342686996111878133300549, b ≈ 2.0223594019664291689707605 and k is an integer from 0 to 12.