Snub digonal-square prismantiprismoid

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Snub digonal-square prismantiprismoid
File:Snub digonal-square prismantiprismoid.png
Rank4
TypeIsogonal
Elements
Cells32+32 irregular tetrahedra, 16 phyllic disphenoids, 8 rhombic disphenoids, 8 tetragonal disphenoids, 4 square gyroprisms, 4 square antiprisms
Faces32+32+32+32+32+32 scalene triangles, 32 isosceles triangles, 8 squares
Edges16+16+16+16+32+32+32
Vertices32
Vertex figurePolyhedron with 2 tetragons and 12 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualSemistellated digonal-square tegmoantitegmoid
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(B2×I2(8))/2+, order 32
ConvexYes
NatureTame

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.