The Doctor is summoned back to the planet Tigella, where the population is divided along religious and scientific lines. Something is going terribly wrong with Tigella's main power source, the Dodecahedron, but the Savants are prevented from investigating by the zealous Deons. To make matters worse, before the Doctor can solve the problem with the Dodecahedron, he is accused of its theft. The true culprit is Meglos, a shapeshifting Zolfa-Thuran, who intends to unleash the full might of the Dodecahedron upon the universe.