19-3 step prism
|19-3 step prism|
|Symmetry||I2(19)+×2×I, order 38|
|Vertex figure||14-vertex polyhedron with 24 triangular faces|
|Cells||19+19+19+19+19+19 phyllic disphenoids|
|Faces||19+19+38+38+38+38+38 scalene triangles|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||12-valence (19):|
The 19-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 114 phyllic disphenoids of six kinds as cells, with 24 joining at each vertex. It can also be constructed as the 19-6 step prism.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 19-3 step prism inscribed in an enneadecagonal duoprism with base lengths a and b are given by:
- (a*sin(2πk/19), a*cos(2πk/19), b*sin(6πk/19), b*cos(6πk/19)),
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: ≈ 1:1.83802.
[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".