Two novel hybrid uranyl peroxide phosphate cage clusters, designated U20P6 and U20P12, contain peroxide bridges between uranyl in an unusual mu-eta(1):eta(2) configuration, as well as the common mu-eta(1):eta(2) configuration. These appear to be the only high-nuclearity metal peroxide complexes containing mu-eta(1):eta(2) peroxide bridges, and they are unique among uranyl peroxide cages. Both clusters contain 20 uranyl polyhedra, and U20P6 and U20P12 contain 6 and 12 phosphate tetrahedra, respectively. The 20 uranyl polyhedra in both cages are arranged on the vertices of distorted topological dodecahedrons (20 vertex fullerenes). Each cage is completed by phosphate tetrahedra and is templated by a sulfate -centered Na-12 cluster with the Na cations defining a regular convex isocahedron. Whereas mu-eta(1):eta(2) peroxides are essential features of uranyl peroxide cages, where they form equatorial edges of uranyl hexagonal bipyramids, the mu-eta(1):eta(2) peroxide groups in U20P6 and U20P12 are associated with strong distortions of the uranyl polyhedra. Formation of U20P6 and U20P12 is a further demonstration of the pliable nature of uranyl polyhedra, which contributes to the tremendous topological variability of uranyl compounds. Despite the unusual structure and highly distorted polyhedral geometries of U20P6, small-angle X-ray scattering and Raman spectra suggest its stability in the aqueous solution and solid state.