Square-hexagonal triswirlprism

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Square-hexagonal triswirlprism
Rank4
TypeIsogonal
Elements
Cells72+72 phyllic disphenoids, 18 square gyroprisms, 12 hexagonal gyroprisms
Faces144+144+144 scalene triangles, 18 squares, 12 hexagons
Edges72+72+72+72+72
Vertices72
Vertex figure10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on square-hexagonal duoprisms of edge length 1)
Edge lengthsShort side edges (72):
 Medial side edges (72):
 Long side edges (72):
 Edges of squares (72): 1
 Edges of hexagons (72): 1
Circumradius
Central density1
Related polytopes
DualSquare-hexagonal triswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(12)×I2(18))+/3, order 144
ConvexYes
NatureTame

The square-hexagonal triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 12 hexagonal gyroprisms, 18 square gyroprisms, and 144 phyllic disphenoids of two kinds. 2 hexagonal gyroprisms, 2 square gyroprisms, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal-octadecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.63274.