15-4 step prism
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|15-4 step prism|
|File:15-4 step prism.png|
|Cells||30+30 phyllic disphenoids|
|Faces||60 scalene triangles, 30+30 isosceles triangles|
|Vertex figure||Paratetraaugmented digonal scalenohedron|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||6-valence (30):|
|Abstract & topological properties|
|Symmetry||S2(I2(15)-4)×2R, order 60|
The 15-4 step prism is a convex isogonal polychoron and a member of the step prism family. It has 60 phyllic disphenoids of two kinds as cells, with 16 joining at each vertex.
Compared to other 15-vertex step prisms, this polychoron has doubled symmetry, because 15 is a factor of 42-1 = 15.
The ratio between the longest and shortest edges is 1: ≈ 1:1.39239.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 15-4 step prism of circumradius √2 are given by:
- (sin(2πk/15), cos(2πk/15), sin(8πk/15), cos(8πk/15)),
where k is an integer from 0 to 14.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".