Snub digonal-square prismantiprismoid
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Snub digonal-square prismantiprismoid | |
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File:Snub digonal-square prismantiprismoid.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 32+32 irregular tetrahedra, 16 phyllic disphenoids, 8 rhombic disphenoids, 8 tetragonal disphenoids, 4 square gyroprisms, 4 square antiprisms |
Faces | 32+32+32+32+32+32 scalene triangles, 32 isosceles triangles, 8 squares |
Edges | 16+16+16+16+32+32+32 |
Vertices | 32 |
Vertex figure | Polyhedron with 2 tetragons and 12 triangles |
Measures (edge length 1) | |
Central density | 1 |
Related polytopes | |
Dual | Semistellated digonal-square tegmoantitegmoid |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (B2×I2(8))/2+, order 32 |
Convex | Yes |
Nature | Tame |
The snub digonal-square prismantiprismoid is a convex isogonal polychoron that consists of 4 square antiprisms, 4 square gyroprisms, 8 tetragonal disphenoids, 8 rhombic disphenoids, 16 phyllic disphenoids, and 64 irregular tetrahedra of two kinds. 1 square antiprism, 1 square gyroprism, 1 tetragonal disphenoid, 1 rhombic disphenoid, 2 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained from the process of alternating a digonal-square truncatoprismantiprismoid. However, it cannot be made uniform.
This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.55377) would yield a square-square duoantiprism instead.