12-5 double gyrostep prism

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12-5 double gyrostep prism
File:12-5 double gyrostep prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells24+24+24 phyllic disphenoids, 48 irregular tetrahedra
Faces24+24 isosceles triangles, 48+48+48+48 scalene triangles
Edges24+24+24+24+48
Vertices24
Vertex figure12-vertex polyhedron with 20 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
Dual12-5 antibigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)+×4×I, order 48
ConvexYes
NatureTame

The 12-5 double gyrostep prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids and 48 irregular tetrahedra. 12 phyllic disphenoids and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (a/b = ) would yield a 24-5 step prism instead.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 12-5 double gyrostep prism are given by:

  • (a*sin(2πk/12), a*cos(2πk/12), b*sin(10πk/12), b*cos(10πk/12)),
  • (b*sin(2πk/12), b*cos(2πk/12), a*sin(10πk/12), a*cos(10πk/12)),

where a/b is greater than 2-3 but less than 23+14-83-3 and k is an integer from 0 to 11.

External links[edit | edit source]