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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. The Doctor demonstrated how this could be done to Leela, by using two boxes of different size. He placed the larger box on the TARDIS console, and then walked to stand next to Leela and asked which one was bigger, which was pointed out by Leela, to which the Doctor stated it was smaller which was because of the distance. The Doctor said that if the large box was kept away at that distance, and had it nearby the larger box would fit inside the smaller box. Leela called that "silly," much to the Doctor's annoyance.(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)