Acronym  ... 
Name  Wells' "hyperbolic" {4,5} polyhedron 
©  
Vertex figure  [4^{5}] (nonregular, nonflat) 
Dihedral angles
(at margins) 

Despite of being uniform and additionally having a single face shape only, these fall into different classes of symmetry.
This uniform skew polyhedron looks like being obtained from all the squares of a structure, built of interlocking squobcues. None the less those aren't true according Johnson solids, rather those are variants thereof. In fact the axial height h of those bicupolae has to be chosen such that it matches to the equatorial triangletriangle edges c, while all squares remain regular. This then amounts in values c = h = 2/sqrt(3) = 1.154701 > 1
(N → ∞) 4N  2 2 1  1 4 ++ 2  4N * *  1 1 base edges 2  * 4N *  0 2 lacing edges 2  * * 2N  0 2 equatorial edges ++ 4  4 0 0  N * base squares of orthobicupolae 4  1 2 1  * 4N lacing squares of orthobicupolae
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