Square duotruncatoalterprism

Square duotruncatoalterprism
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	16 tetragonal disphenoids, 16 rectangular trapezoprisms, 16 square cupolas, 8 square prisms
Faces	64 isosceles triangles, 64 isosceles trapezoids, 32 rectangles, 16 squares, 8 ditetragons
Edges	32+32+64+64
Vertices	64
Vertex figure	Monoaugmented isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Square duotruncatoaltertegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	Yes
Nature	Tame

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.