Square antiditetragoltriate

Square antiditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Squaddet
Elements
Cells	16+16 tetragonal disphenoids, 32 rectangular pyramids, 8 square prisms
Faces	64+64 isosceles triangles, 8 squares, 32 rectangles
Edges	32+32+64
Vertices	32
Vertex figure	Biaugmented triangular prism
Measures (based on same duoprisms as optimized square ditetragoltriate)
Edge lengths	Edges of smaller square (32): 1
	Lacing edges (64): $\sqrt{5-2\sqrt2} ≈ 1.47363$
	Edges of larger square (32): 2
Circumradius	$\frac{\sqrt{10}}{2} ≈ 1.58114$
Central density	1
Related polytopes
Army	Squaddet
Regiment	Squaddet
Dual	Square antitetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	Yes
Nature	Tame

The square antiditetragoltriate or squaddet is a convex isogonal polychoron and the second member of the antiditetragoltriate family. It consists of 8 square prisms, 32 rectangular pyramids, and 32 tetragonal disphenoids of two kinds. 2 square prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform square duoprisms where the larger square is more than $\sqrt2$ times the edge length of the smaller one.