Transitional square double triswirlprism
Transitional square double triswirlprism | |
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File:Transitional square double triswirlprism.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 48 tetragonal disphenoids, 96 tetragonal antiwedges, 24 square gyroprisms |
Faces | 192+192 scalene triangles, 96 isosceles trapezoids, 24 squares |
Edges | 48+96+96+96+96 |
Vertices | 96 |
Vertex figure | 9-vertex polyhedron with 4 tetragons and 6 triangles |
Measures (edge length 1) | |
Central density | 1 |
Related polytopes | |
Dual | Transitional square double triswirltegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(12)≀S2)+/3, order 192 |
Convex | Yes |
Nature | Tame |
The transitional square double triswirlprism is a convex isogonal polychoron that consists of 24 square gyroprisms, 96 tetragonal antiwedges, and 48 tetragonal disphenoids. 2 square gyroprisms, 6 tetragonal antiwedges, and 2 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal square-square triswirlprisms based on squares of different edge length. However, it cannot be made uniform. It is the third in an infinite family of isogonal square prismatic swirlchora, the others being the small square double triswirlprism and great square double triswirlprism.
The ratio between the longest and shortest edges is 1: ≈ 1:1.36603.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a transitional square double triswirlprism are given as Cartesian products of the vertices of two squares S1 and S2 with length ratio 1: ≈ 1:1.73205:
- S1 × S2,
- S3 × S4 (S1 and S2 both rotated 30 degrees),
- S5 × S6 (S1 and S2 both rotated 60 degrees),
- S2 × S1,
- S4 × S3,
- S6 × S5.