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A dodecahedron was a twelve-sided regular polyhedron, with each side a pentagon.
The Zolfa-Thuran, Meglos, wished to steal it and use its power to conquer and destroy worlds. Under the guise of the Fourth Doctor, Meglos compressed the Dodecahedron and stole it. He took it back to Zolfa-Thura.
Using the Screens of Zolfa-Thura, Meglos was able to boost the Dodecahedron's power. He planned to destroy Tigella with it but the Doctor reverted the calculations so it destroyed Zolfa-Thura. (TV: Meglos)