17-4 step prism
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|17-4 step prism|
|File:17-4 step prism.png|
|Cells||34+34 phyllic disphenoids, 17 tetragonal disphenoids|
|Faces||68 scalene triangles, 34+68 isosceles triangles|
|Vertex figure||Paratetraaugmented triakis tetragonal disphenoid|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||8-valence (34):|
|Abstract & topological properties|
|Symmetry||S2(I2(17)-4)×2I, order 68|
The 17-4 step prism is a convex isogonal polychoron, member of the step prism family. It has 17 tetragonal disphenoids and 68 phyllic disphenoids of two kinds as cells. 2 tetragonal and 16 phyllic disphenoids join at each vertex.
Compared to other 17-vertex step prisms, this polychoron has doubled symmetry, because 17 is a factor of 42+1 = 17.
The ratio between the longest and shortest edges is 1: ≈ 1:1.51687.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 17-4 step prism of circumradius √2 are given by:
- (sin(2πk/17), cos(2πk/17), sin(8πk/17), cos(8πk/17)),
where k is an integer from 0 to 16.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".