40-9 step prism
The 40-9 step prism, also known as the digonal double pentaswirlprism, is a convex isogonal polychoron, member of the step prism family. It has 40 rhombic disphenoids and 240 phyllic disphenoids of three kinds as cells. 4 rhombic and 24 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal digonal prismatic swirlchora.
| 40-9 step prism | |
|---|---|
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 80+80+80 phyllic disphenoids, 40 rhombic disphenoids |
| Faces | 160+160+160 scalene triangles, 80 isosceles triangles |
| Edges | 40+40+80+80+80 |
| Vertices | 40 |
| Vertex figure | 16-vertex polyhedron with 28 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | 40-9 gyrochoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | S2(I2(40)-9)×2R, order 160 |
| Convex | Yes |
| Nature | Tame |
The ratio between the longest and shortest edges is 1: ≈ 1:2.28825.
Vertex coordinates edit
Coordinates for the vertices of a 40-9 step prism of circumradius √2 are given by:
- (sin(πk/20), cos(πk/20), sin(9πk/20), cos(9πk/20)),
where k is an integer from 0 to 39.