Transitional square double triswirlprism

From Polytope Wiki
Jump to navigation Jump to search
Transitional square double triswirlprism
File:Transitional square double triswirlprism.png
Rank4
TypeIsogonal
Elements
Cells48 tetragonal disphenoids, 96 tetragonal antiwedges, 24 square gyroprisms
Faces192+192 scalene triangles, 96 isosceles trapezoids, 24 squares
Edges48+96+96+96+96
Vertices96
Vertex figure9-vertex polyhedron with 4 tetragons and 6 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualTransitional square double triswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(12)≀S2)+/3, order 192
ConvexYes
NatureTame

The transitional square double triswirlprism is a convex isogonal polychoron that consists of 24 square gyroprisms, 96 tetragonal antiwedges, and 48 tetragonal disphenoids. 2 square gyroprisms, 6 tetragonal antiwedges, and 2 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal square-square triswirlprisms based on squares of different edge length. However, it cannot be made uniform. It is the third in an infinite family of isogonal square prismatic swirlchora, the others being the small square double triswirlprism and great square double triswirlprism.

The ratio between the longest and shortest edges is 1: ≈ 1:1.36603.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a transitional square double triswirlprism are given as Cartesian products of the vertices of two squares S1 and S2 with length ratio 1: ≈ 1:1.73205:

  • S1 × S2,
  • S3 × S4 (S1 and S2 both rotated 30 degrees),
  • S5 × S6 (S1 and S2 both rotated 60 degrees),
  • S2 × S1,
  • S4 × S3,
  • S6 × S5.