19-7 step prism
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19-7 step prism | |
---|---|
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 19+19+19+19 phyllic disphenoids |
Faces | 38+38+38 scalene triangles, 19+19 isosceles triangles |
Edges | 19+19+19+19+19 |
Vertices | 19 |
Vertex figure | Edge-expanded heptagonal tegum |
Measures (circumradius , based on a uniform duoprism) | |
Edge lengths | 7-valence (19): |
5-valence (19): | |
4-valence (19): | |
4-valence (19): | |
4-valence (19): | |
Central density | 1 |
Related polytopes | |
Dual | 19-7 gyrochoron |
Abstract & topological properties | |
Flag count | 1824 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | S2(I2(19)-7), order 38 |
Convex | Yes |
Nature | Tame |
The 19-7 step prism is a convex isogonal polychoron and a member of the step prism family. It has 76 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 19-8 step prism. It is also the heptagonal funk tegum.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.67674.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 19-7 step prism inscribed in an enneadecagonal duoprism with base lengths a and b are given by:
- ,
where k is an integer from 0 to 18. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:1.06046.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".