Square-ditetragonal duoprismatic cupoliprism

Square-ditetragonal duoprismatic cupoliprism
Rank	5
Type	Isogonal
Notation
Coxeter diagram	xo4xx ox4xx&#y
Elements
Tera	8 square cupofastegiums, 8 square cupolic prisms, 2 square-ditetragonal duoprisms
Cells	16 tetragonal disphenoids, 32 wedges, 16 square cupolas, 16 cuboids, 8+8 square prisms, 8 ditetragonal prisms
Faces	64 isosceles triangles, 64 isosceles trapezoids, 32+32 rectangles, 16 squares, 8 ditetragons
Edges	32+32+64+64
Vertices	64
Vertex figure	Isosceles-trapezoidal pyramidal pyramid
Measures (base edge lengths 1, height h)
Circumradius	${\frac {\sqrt {6+2{\sqrt {2}}+h^{2}}}{2}}$
Central density	1
Related polytopes
Dual	Square-tetrambic duotegmatic cupolitegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B2▲S2, order 128
Convex	Yes
Nature	Tame

The square-ditetragonal duoprismatic cupoliprism is a convex isogonal polyteron and a member of the duoprismatic cupoliprism family. It consists of 2 square-ditetragonal duoprisms, 8 square cupolic prisms, and 8 square cupofastegiums. 1 square-ditetragonal duoprism, 3 square cupolic prisms, and 2 square cupofastegiums join at each vertex. However, it cannot be made scaliform, because the height between the two bases is 0 if all edges are of the same length, making it a small disprismatotesseractihexadecachoron (or square duoexpandoprism) instead.