A Transportalizer is a pedestal-shaped device used to transport people and objects to other places. The central stairwell of Jade's house features a series of Transportalizers (Jade almost never uses the stairs). There is also one located in the Skaianet Laboratory near Rose's house, which, in Act 3, Jaspers's body is accidentally teleported by.
Various Transportalizers can be found throughout the Planets in The Medium, and one was shown to be on Derse. So far, all of these lead to the ectobiology lab in the Veil.
Curiously, it features the pattern of a fractal, one similar to those on the Alchemiter and Appearifier.
The post-scratch kids' Frog Temple contains two transportalizers, one yellow and one purple. They allow travel to Prospit and Derse, which would explain how Grandma was able to steal the fourth wall from Derse and bring it to Earth (and, if the transportalizers are in all incarnations of the Temple, would explain how Grandpa did the same). Another transportalizer was found on LOCAH, which was also shown to lead to Derse.
Post-scratch Prospit has two smaller transportalizers for each cell in their prisons; one for receiving food, and one for disposing of waste. Derse used to have transportalizers as well for its waste disposal, before phasing them out because too many of their prisoners committed suicide by transportalizing their own head. Jack, after just murdering a brave warrior in cold blood, modifiesthe transportalizer in his cell to send the decapitated head of said brave warrior to the White Queen, to honor his memory.