Square duotruncatoalterprism

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Square duotruncatoalterprism
Rank4
TypeIsogonal
Elements
Cells16 tetragonal disphenoids, 16 rectangular trapezoprisms, 16 square cupolas, 8 square prisms
Faces64 isosceles triangles, 64 isosceles trapezoids, 32 rectangles, 16 squares, 8 ditetragons
Edges32+32+64+64
Vertices64
Vertex figureMonoaugmented isosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
DualSquare duotruncatoaltertegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2≀S2, order 128
ConvexYes
NatureTame

The square duotruncatoalterprism is a convex isogonal polychoron and the third member of the duotruncatoalterprism family. It consists of 8 square prisms, 16 square cupolas, 16 rectangular trapezoprisms, and 16 tetragonal disphenoids. 1 square prism, 3 square cupolas, 2 rectangular trapezoprisms, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal square-ditetragonal duoprisms. However, it cannot be made scaliform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:2) would yield a square duotransitionalterprism instead.