The uniform polyhedron compounds were first enumerated by John Skilling in 1976, with a proof that the enumeration is complete. The following table lists them according to his numbering.
The prismatic compounds of {p/q}-gonalprisms (UC20 and UC21) exist only when p/q > 2, and when p and q are coprime. The prismatic compounds of {p/q}-gonalantiprisms (UC22, UC23, UC24 and UC25) exist only when p/q > 3/2, and when p and q are coprime. Furthermore, when p/q = 2, the antiprisms degenerate into tetrahedra with digonal bases.
Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79: 447–457, doi:10.1017/S0305004100052440, MR0397554.