In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts transitively on the compound's vertices.
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 prisms (UC<sub>20</sub> and UC<sub>21</sub>) exist only when , and when and are coprime. The uniform prismatic compounds of antiprisms (UC<sub>22</sub>, UC<sub>23</sub>, UC<sub>24</sub> and UC<sub>25</sub>) exist only when , and when and are coprime. Furthermore, when , the antiprisms degenerate into tetrahedra with digonal bases.