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This uniform polyhedron compound is a symmetric arrangement of 3 square antiprisms, aligned with the three axes of 4-fold rotational symmetry of a cube.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the even permutations of
(±√(√2+1), ±√(√2−1), ±1)with an even number of minuses in the '±' choices, together with all the odd permutations with an odd number of minuses in the '±' choices.
References
Compound of three square antiprisms Wikipedia(Text) CC BY-SA