On Tigella, two opposing factions are irrevocably divided over one fundamental issue: the Dodecahedron, a mysterious artefact which provides the entire planet's energy. With the Savants and the Deons locked in a crippling stalemate, and their civilisation on the brink of collapse, the Tigellan leader Zastor seeks the Doctor's help. But the Doctor and Romana have been trapped aboard the TARDIS in a timeloop by Meglos, the last of the Zolpha Thurans, who will stop at nothing to steal back the awesome power of the Dodecahedron.