Most of the serial refers to the generic "third planet", only calling it the "Planet of Evil" in the last episode, which sounds more specific. The novelization treats "Planet of Evil" as a definite name. "Third planet" should stay as a redirect.
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The Planet of Evil, also referred to as the third planet, was a black asteroid, (PROSE: Doctor Who and the Armageddon Factor) an artificial planet that served as the domain of the Shadow and his Mutes, described as the "valley of the Shadow". The planet had four claw-like prongs and a rocky interior which could generate illusions, with transmat links to Zeos and Atrios.
For five years in the far future, the third planet was positioned over a million miles away from Atrios, blocking it's view of Zeos as the Shadow, using the computer Mentalis built by Drax under threat, waged a war between the two planets in order to obtain the sixth segment of the Key to Time for the Black Guardian. Meanwhile, Drax hid in tunnels on the planet, transmitting an intergalactic computer distress signal for help.
Using the Marshal of Atrios's nuclear missiles aimed at Zeos, the Fourth Doctor set up a deflective forcefield for a millisecond, bouncing the missiles off of Zeos and smack at the Planet of Evil, destroying it along with the Shadow and the Mutes. (TV: The Armageddon Factor)