Great 12-5 double step prism
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| Great 12-5 double step prism | |
|---|---|
| File:Great 12-5 double step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Cells | 12 tetragonal disphenoids, 12+12 rhombic disphenoids, 24 phyllic disphenoids, 48+48 irregular tetrahedra |
| Faces | 24 isosceles triangles, 48+48+48+48+48+48 scalene triangles |
| Edges | 12+24+24+24+24+24+48 |
| Vertices | 24 |
| Vertex figure | 15-vertex polyhedron with 26 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Great 12-5 bigyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | I2(12)+×4×I, order 48 |
| Convex | Yes |
| Nature | Tame |
The great 12-5 double step prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids, and 96 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 rhombic disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.
This polychoron cannot be optimized using the ratio method, because the solution (a/b = √33+12√7/3) would yield a small 12-5 double step prism instead.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a great 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/b is greater than 7-4√3 but less than 2-√3 and k is an integer from 0 to 11.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".