12-4 step prism
|12-4 step prism|
|Symmetry||I2(12)+×2×I, order 24|
|Vertex figure||Tetragonal antiwedge|
|Cells||12 phyllic disphenoids, 3 square antiprisms|
|Faces||12 isosceles triangles, 24 scalene triangles, 3 squares|
|Measures (circumradius , based on a unit duoprism)|
|Edge lengths||3-valence (12):|
|3-valence (12): 2|
The 12-4 step prism is a convex isogonal polychoron and member of the step prism family. It has 3 chiral square antiprisms and 12 phyllic disphenoids as cells, with 4 disphenoids and 2 antiprisms joining at each vertex.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.16877.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 12-4 step prism inscribed in a dodecagonal duoprism with base lengths a and b are given by:
- (a*sin(πk/6), a*cos(πk/6), b*sin(2πk/3), b*cos(2πk/3)),
where k is an integer from 0 to 11. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:0.75984.
Isogonal derivatives[edit | edit source]
- Phyllic disphenoid (12): 12-4 step prism
- Scalene triangle (12): 12-4 step prism
- Scalene triangle (24): 24-4 step prism
- Edge (12): 12-4 step prism
[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".