Great transitional 12-5 double step prism
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|Great transitional 12-5 double step prism|
|File:Great transitional 12-5 double step prism.png|
|Cells||24+48 phyllic disphenoids, 12+12 rhombic disphenoids, 12 chiral digonal scalenohedra|
|Faces||48+48+48+48+48 scalene triangles|
|Vertex figure||13-vertex polyhedron with 3 tetragons and 16 triangles|
|Measures (edge length 1)|
|Dual||Great transitional 12-5 bigyrochoron|
|Abstract & topological properties|
|Symmetry||S2(I2(12)-5)×2R, order 48|
The great transitional 12-5 double step prism is a convex isogonal polychoron that consists of 12 chiral digonal scalenohedra, 24 rhombic disphenoids of two kinds, and 72 phyllic disphenoids of two kinds. 3 digonal scalenohedra, 4 rhombic disphenoids, and 12 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.
The ratio between the longest and shortest edges is 1: ≈ 1:2.73861.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a great transitional 12-5 double step prism are given by:
- (a*sin(2πk/12), a*cos(2πk/12), b*sin(10πk/12), b*cos(10πk/12)),
- (b*sin(2πk/12), b*cos(2πk/12), a*sin(10πk/12), a*cos(10πk/12)),
where a = (2-√3)/2, b = (2+√3)/2 and k is an integer from 0 to 11.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".