Triangular-pentagonal tetraswirlprism
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Triangular-pentagonal tetraswirlprism | |
---|---|
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 60+60+60 phyllic disphenoids, 20 triangular gyroprisms, 12 pentagonal gyroprisms |
Faces | 120+120+120+120 scalene triangles, 20 triangles, 12 pentagons |
Edges | 60+60+60+60+60+60 |
Vertices | 60 |
Vertex figure | 12-vertex polyhedron with 4 tetragons and 12 triangles |
Measures (based on triangular-pentagonal duoprisms of edge length 1) | |
Edge lengths | Side 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 density | 1 |
Related polytopes | |
Dual | Triangular-pentagonal tetraswirltegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(12)×I2(20))+/4, order 120 |
Convex | Yes |
Nature | Tame |
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.