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Transdimensional engineering was the technology of creating dimensionally transcendental objects, which the Fourth Doctor proclaimed a "key Time Lord discovery". It was used to make TARDISes bigger on the inside. (TV: The Robots of Death)

When Missy settled down the 3W Institute inside St Paul's Cathedral, with a group of 91 Cybermen, the Twelfth Doctor explained that nobody noticed thanks to "dimensional engineering — one space folded inside another". (TV: Death in Heaven)

Other than the Time Lords, the Daleks (TV: The Chase, The Evil of the Daleks) and Mawdryn's people, who sought to emulate the Time Lords, had developed this technology and employed it in their transmat capsules. (TV: Mawdryn Undead) The Genesis Ark was known as "Time Lord science", which the Tenth Doctor elaborated was a prison ship which was bigger on the inside. (TV: Doomsday)

The War Lords possessed dimensionally transcendental space-time vessels known as SIDRATs, though only those provided by a renegade Time Lord, the War Chief. (TV: The War Games)