A design for ultra-high efficiency solar modules (>50%) using spectrum splitting is proposed. In the polyhedral specular reflector design, seven subcells are arranged around a solid parallelepiped. Incident light enters the parallelepiped and is directed via specular reflection onto each subcell in order from highest to lowest bandgap. We analyze optical losses due to external concentration and parasitic absorption and optimize the design for >50% module efficiency. We find that moderate concentration designs (90–170x) with a high index parallelepiped and perfect shortpass filters meet target efficiencies and demonstrate an initial design.