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A dimensionally transcendental (sometimes called transcendentally dimensional) object was one which appeared larger inside than outside, an effect made possible by transcendental engineering.
The Fourth Doctor once explained the principle to Leela by using the analogy of how a larger cube might appear to be able to fit inside a smaller one were the larger cube further away, yet immediately accessible at the same time. He described this as "a key Time Lord discovery". (TV: The Robots of Death) Rory Williams later surprised the Doctor with his understanding of the principle, that the inside was "basically another dimension." (TV: The Vampires of Venice)
The relationship between the interior and exterior sizes of a TARDIS could be controlled via the dimensional stabiliser. (TV: The Time Meddler) Known dimensionally transcendental objects other than TARDISes included Dalek time machines, the SIDRATs constructed by the War Chief, the Genesis Ark, the Doctor's pockets, and The Towers of Canonicity and Likelihood on Gallifrey. (TV: The Chase, The War Games, Doomsday, The Runaway Bride, The Vampires of Venice; PROSE: The Gallifrey Chronicles)
Some of the Doctor's incarnations had a habit of pulling a wide array of items from their pockets, presumably an effect of dimensional transcendentalism. These incarnations included the Second, Third, Fourth, Seventh, Tenth and Eleventh Doctors. It was also known that the Daleks were capable of creating dimensionally transcendent factory ships. (PROSE: War of the Daleks)
The Doctor temporarily expanded the interior dimensions of a boarding house in Cheldon Bonniface to allow all the guests at Benny's wedding to stay there. (PROSE: Happy Endings)
Upon discovering the large subterranean (and thus hidden) portion of the PhiCorp warehouse, Jack Harkness remarked that it was "bigger on the inside", although he was presumed to be referring simply to the fact that much of warehouse was concealed from the exterior, rather than to true dimensional transcendentalism. (TV: Dead of Night)
Upon meeting the Teselecta, "a robot worked by tiny people", the Eleventh Doctor, wondering how they could all fit inside, briefly suggested that it was bigger on the inside until he discovered it was via basic miniaturisation sustained by a compression field. (TV: Let's Kill Hitler)