Square-hexagonal triswirlprism
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Square-hexagonal triswirlprism | |
---|---|
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 72+72 phyllic disphenoids, 18 square gyroprisms, 12 hexagonal gyroprisms |
Faces | 144+144+144 scalene triangles, 18 squares, 12 hexagons |
Edges | 72+72+72+72+72 |
Vertices | 72 |
Vertex figure | 10-vertex polyhedron with 4 tetragons and 8 triangles |
Measures (based on square-hexagonal duoprisms of edge length 1) | |
Edge lengths | Short side edges (72): |
Medial side edges (72): | |
Long side edges (72): | |
Edges of squares (72): 1 | |
Edges of hexagons (72): 1 | |
Circumradius | |
Central density | 1 |
Related polytopes | |
Dual | Square-hexagonal triswirltegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(12)×I2(18))+/3, order 144 |
Convex | Yes |
Nature | Tame |
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.