13-5 step prism
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|13-5 step prism|
|File:13-5 step prism.png|
|Cells||26 phyllic disphenoids, 13 tetragonal disphenoids|
|Faces||26+52 isosceles triangles|
|Vertex figure||Prodigonal antiprismatic symmetric snub disphenoid|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||5-valence (26):|
|Abstract & topological properties|
|Symmetry||S2(I2(13)-5)×2I, order 52|
The 13-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 13 tetragonal disphenoids and 26 phyllic disphenoids as cells. 4 tetragonal and 8 phyllic disphenoids join at each vertex. It is also the pentagonal funk tegum.
Compared to other 13-vertex step prisms, this polychoron has doubled symmetry, because 13 is a factor of 52+1 = 26.
Its vertex figure is topologically equivalent to the Johnson solid snub disphenoid.
The ratio between the longest and shortest edges is 1: ≈ 1:1.19192.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 13-5 step prism of circumradius √2 are given by:
- (sin(2πk/13), cos(2πk/13), sin(10πk/13), cos(10πk/13)),
where k is an integer from 0 to 12.
Isogonal derivatives[edit | edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
- Tetragonal disphenoid (13): 13-5 step prism
- Edge (26): Small 13-5 double step prism
- Edge (26): Small 13-5 double gyrostep prism
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".