Small 12-5 double step prism
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| Small 12-5 double step prism | |
|---|---|
| File:Small 12-5 double step prism.png | |
| Rank | 4 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Cells | 48 irregular tetrahedra, 24 phyllic disphenoids, 12+12 rhombic disphenoids, 12 tetragonal disphenoids |
| Faces | 24+48 isosceles triangles, 48+48+48 scalene triangles |
| Edges | 12+24+24+24+24+24 |
| Vertices | 24 |
| Vertex figure | 11-vertex polyhedron with 18 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Small 12-5 bigyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | S2(I2(12)-5)×2R, order 48 |
| Convex | Yes |
| Nature | Tame |
The small 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 48 irregular tetrahedra. 2 tetragonal disphenoid, 4 rhombic disphenoids, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.70166.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a small 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 = √7-2√7+√33-12√7/4, b = √7+2√7+√33+12√7/4 and k is an integer from 0 to 11.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".