18-3 step prism
|18-3 step prism|
|Symmetry||I2(18)+×2×I, order 36|
|Vertex figure||Base-tritriakis tetragonal antiwedge|
|Cells||18+18+18+18 phyllic disphenoids, 6 triangular antiprisms|
|Faces||6 triangles, 18+36+36+36+36 scalene triangles|
|Measures (circumradi , based on a uniform duoprism)|
|Edge lengths||10-valence (18):|
The 18-3 step prism, also known as the 9-3 double step prism, is an isogonal polychoron and a member of the step prism family. It has 6 triangular antiprisms and 72 phyllic disphenoids of four kinds as cells, with 16 disphenoids and 2 antiprisms joining at each vertex.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an 18-3 step prism inscribed in an octadecagonal duoprism with base lengths a and b are given by:
- (a*sin(πk/9), a*cos(πk/9), b*sin(πk/3), b*cos(πk/3)),
where k is an integer from 0 to 17. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:1.69688.
[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".