Triangular-square triswirlprism
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Triangular-square triswirlprism | |
---|---|
File:Triangular-square triswirlprism.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 36+36 phyllic disphenoids, 12 triangular gyroprisms, 9 square gyroprisms |
Faces | 72+72+72 scalene triangles, 12 triangles, 9 squares |
Edges | 36+36+36+36+36 |
Vertices | 36 |
Vertex figure | 10-vertex polyhedron with 4 tetragons and 8 triangles |
Measures (based on triangular-square duoprisms of edge length 1) | |
Edge lengths | Short side edges (36): |
Medial side edges (36): | |
Long side edges (36): | |
Edges of triangles (36): 1 | |
Edges of squares (36): 1 | |
Circumradius | |
Central density | 1 |
Related polytopes | |
Dual | Triangular-square triswirltegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(9)×I2(12))+/3, order 72 |
Convex | Yes |
Nature | Tame |
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).