Triangular-square triswirlprism

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Triangular-square triswirlprism
File:Triangular-square triswirlprism.png
Rank4
TypeIsogonal
Elements
Cells36+36 phyllic disphenoids, 12 triangular gyroprisms, 9 square gyroprisms
Faces72+72+72 scalene triangles, 12 triangles, 9 squares
Edges36+36+36+36+36
Vertices36
Vertex figure10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on triangular-square duoprisms of edge length 1)
Edge lengthsShort side edges (36):
 Medial side edges (36):
 Long side edges (36):
 Edges of triangles (36): 1
 Edges of squares (36): 1
Circumradius
Central density1
Related polytopes
DualTriangular-square triswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(9)×I2(12))+/3, order 72
ConvexYes
NatureTame

The triangular-square triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 9 square gyroprisms, 12 triangular gyroprisms, and 72 phyllic disphenoids of two kinds. 2 square gyroprisms, 2 triangular gyroprisms, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the enneagonal-dodecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.85713.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular-square triswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of square S1 and triangle T2 with length ratio 1:1:

  • S1 × T2,
  • S3 × T4 (S1 rotated 30 degrees and T2 rotated 40 degrees),
  • S5 × T6 (S1 rotated 60 degrees and T2 rotated 80 degrees).