15-5 step prism

From Polytope Wiki
Jump to navigation Jump to search
15-5 step prism
15-5 step prism.png
Cells15 phyllic disphenoids, 3 pentagonal gyroprisms
Faces30 scalene triangles, 15 isosceles triangles, 3 pentagons
Vertex figureTetragonal antiwedge
Measures (circumradius , based on a unit duoprism)
Edge lengths3-valence (15):
 4-valence (15):
 3-valence (15):
Central density1
Related polytopes
Dual15-5 gyrochoron
Abstract & topological properties
Euler characteristic0
SymmetryS2(I2(15)-5), order 30

The 15-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 3 pentagonal gyroprisms and 15 phyllic disphenoids as cells, with 4 phyllic disphenoids and 2 pentagonal gyroprisms joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.16349.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 15-5 step prism inscribed in a pentadecagonal duoprism with base lengths a and b are given by:

  • (a*sin(2πk/15), a*cos(2πk/15), b*sin(2πk/3), b*cos(2πk/3)),

where k is an integer from 0 to 14. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:0.63484.

Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

  • Phyllic disphenoid (15): 15-5 step prism
  • Scalene triangle (15): 15-5 step prism
  • Scalene triangle (30): 30-5 step prism
  • Edge (15): 15-5 step prism

External links[edit | edit source]