Triangular-pentagonal tetraswirlprism

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Triangular-pentagonal tetraswirlprism
Rank4
TypeIsogonal
Elements
Cells60+60+60 phyllic disphenoids, 20 triangular gyroprisms, 12 pentagonal gyroprisms
Faces120+120+120+120 scalene triangles, 20 triangles, 12 pentagons
Edges60+60+60+60+60+60
Vertices60
Vertex figure12-vertex polyhedron with 4 tetragons and 12 triangles
Measures (based on triangular-pentagonal duoprisms of edge length 1)
Edge lengthsSide edge 1 (60):
 Side edge 2 (60):
 Side edge 3 (60):
 Side edge 4 (60):
 Edges of triangles (60): 1
 Edges of pentagons (60): 1
Circumradius
Central density1
Related polytopes
DualTriangular-pentagonal tetraswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(12)×I2(20))+/4, order 120
ConvexYes
NatureTame

The triangular-pentagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 12 pentagonal gyroprisms, 20 triangular gyroprisms, and 180 phyllic disphenoids of three kinds. 2 pentagonal gyroprisms, 2 triangular gyroprisms, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal-icosagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.49884.