Hypercube

Hypercubes were a communication technology used by the Time Lords which resembled cubes; they were used by thinking or speaking to them and then sent through time and space. They could be used by humans as well as Time Lords. (EDA: Vampire Science, The Ancestor Cell) They were theoretically impossible to intercept, but a Little Brother of Faction Paradox intercepted a cube the Eighth Doctor sent to the Time Lords. They were mainly owned by members of official Gallifreyan organisations. (EDA: Unnatural History)

Irving Braxiatel once used a hypercube to contact his people. (BNA: Tears of the Oracle)

The First Doctor collected his when he worked for the Bureau of Possible Events, but left them behind on Gallifrey when he escaped with Susan. It was returned to him by his mentor K'anpo Rimpoche shortly before his first regeneration along with his Five Hundred Year Diary. (ST: The Three Paths)

The Second Doctor used a hypercube to ask the Time Lords to return the soldiers kidnapped by the War Lords to their own time periods. (DW: The War Games)

Hundreds of Time Lords, stranded in the bubble universe by House, used hypercubes to send distress calls. The Corsair's hypercube arrived in the main universe and found the Doctor's TARDIS. After the Doctor arrived in the bubble universe, he heard the distress calls on Nephew's translation sphere and thought this meant there were living Time Lords. To his dismay and fury, all the Doctor found was a cabinet filled with hypercubes. House had murdered every Time Lord it had encountered. (DW: The Doctor's Wife)

The Doctor kept a hypercube in the TARDIS Drawing Room. (VG: The Gunpowder Plot)

Behind the scenes

 * In real-world mathematics, a hypercube is a higher-dimensional analogue to a cube, the former having four dimensions, the latter three.