If the cubes are compressed into rhombic prisms, a compound of 3 rhombic prisms is constructed.
The compound has pyritohedral symmetry.

Its vertices are parametrized with lengths a and b with values besides √2.

(±a,  0, ±1), ( 0, ±b, ±1)
(±b, ±1,  0), ( 0, ±1, ±a)
(±1, ±a,  0), (±1,  0, ±b)
If the cubes are compressed into rhombic prisms, a compound of 3 rhombic prisms is constructed. The compound has pyritohedral symmetry.
Its vertices are parametrized with lengths a and b with values besides √2.
(±a,  0, ±1), ( 0, ±b, ±1)
(±b, ±1,  0), ( 0, ±1, ±a)
(±1, ±a,  0), (±1,  0, ±b)
Compound of three cubes