13-2 step prism
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13-2 step prism | |
---|---|
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 13+13+13+13+13 phyllic disphenoids |
Faces | 26+26+26+26 scalene triangles, 13+13 isosceles triangles |
Edges | 13+13+13+13+13+13 |
Vertices | 13 |
Vertex figure | Ridge-tritriakis bi-apiculated tetrahedron |
Measures (circumradius , based on a uniform duoprism) | |
Edge lengths | 11-valence (13): |
3-valence (13): | |
4-valence (13): | |
4-valence (13): | |
4-valence (13): | |
4-valence (13): | |
Central density | 1 |
Related polytopes | |
Dual | 13-2 gyrochoron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | S2(I2(13)-2), order 26 |
Convex | Yes |
Nature | Tame |
The 13-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 65 phyllic disphenoids of five kinds as cells, with 20 joining at each vertex. It can also be constructed as the 13-6 step prism.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.16752.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 13-2 step prism inscribed in a tridecagonal duoprism with base lengths a and b are given by:
- (a*sin(2πk/13), a*cos(2πk/13), b*sin(4πk/13), b*cos(4πk/13)),
where k is an integer from 0 to 12. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to : ≈ 1:2.41846.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".