Small transitional 12-5 double step prism
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|Small transitional 12-5 double step prism|
|File:Small transitional 12-5 double step prism.png|
|Cells||12 tetragonal disphenoids, 12 rectangular gyroprisms|
|Faces||24+48 isosceles triangles, 12 rectangles|
|Vertex figure||Digonal-rectangular gyronotch|
|Measures (edge length 1)|
|Dual||Small transitional 12-5 bigyrochoron|
|Abstract & topological properties|
|Symmetry||S2(I2(12)-5)×2R, order 48|
The small transitional 12-5 double step prism is a convex isogonal polychoron that consists of 12 rectangular gyroprisms and 12 tetragonal disphenoids. 2 rectangular gyroprisms and 4 tetragonal 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: ≈ 1:1.73205.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a small 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 = (√3-1)/4, b = (1+√3)/4 and k is an integer from 0 to 11.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".