Digonal-square tetraswirlprism
Digonal-square tetraswirlprism | |
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File:Digonal-square tetraswirlprism.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 32+32+32 phyllic disphenoids, 16 rhombic disphenoids, 8 square gyroprisms |
Faces | 64+64+64+64 scalene triangles, 8 squares |
Edges | 16+32+32+32+32+32 |
Vertices | 32 |
Vertex figure | 11-vertex polyhedron with 2 tetragons and 14 triangles |
Measures (based on square prisms of edge length 1) | |
Edge lengths | Side edge 1 (32): |
Side edge 2 (32): | |
Side edge 3 (32): | |
Side edge 4 (32): | |
Digon edges (16): 1 | |
Edges of squares (32): 1 | |
Circumradius | |
Central density | 1 |
Related polytopes | |
Dual | Digonal-square tetraswirltegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(8)×I2(16))+/4, order 64 |
Convex | Yes |
Nature | Tame |
The digonal-square tetraswirlprism, also known as the 16-2 double step prism or 16-6 double step prism, is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 8 square gyroprisms, 16 rhombic disphenoids, and 96 phyllic disphenoids of three kinds. 2 square gyroprisms, 2 rhombic disphenoids, and 12 phyllic disphenoids joined at each vertex. It can be obtained as a subsymmetrical faceting of the octagonal-hexadecagonal duoprism.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.11968.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a digonal-square tetraswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of square S1 and digon D2 with length ratio 1:1:
- S1 × D2,
- S3 × D4 (S1 rotated 22.5 degrees and D2 rotated 45 degrees),
- S5 × D6 (S1 rotated 45 degrees and D2 rotated 90 degrees),
- S7 × D8 (S1 rotated 67.5 degrees and D2 rotated 135 degrees).