Hypercube

Hypercubes were essentially letters sent between Time Lords, but they were white cubes that bore a Time Lord's thoughts or speech. They were then sent through time and space to Gallifrey or to someone they trusted enough to rescue them. They could be used by humans as well as Time Lords. (PROSE: 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. (PROSE: Unnatural History)

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

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, as he could not do so on his own. The Doctor constructed this one from six separate white cards and merged them with his mind. Calling upon his people for help proved to be a personal sacrifice for the Doctor; it led to his exile on Earth, a forced regeneration into the Third Doctor, and the separation from his companions Jamie McCrimmon and Zoe Heriot. (TV: The War Games)

The Fifth Doctor used a hypercube to notify the Time Lords that he had found Zero. (AUDIO: Spring)

Hundreds of Time Lords, stranded in the bubble universe by House, attempted to use hypercubes to send distress calls. However, House killed many or all of them for parts to repair Auntie and Uncle, feeding itself on their TARDISes for five thousand years. One Time Lord to arrive on House was the Doctor's good friend the Corsair. He recorded a hypercube, which was sent into the main universe. It eventually found the Doctor's TARDIS, because there were no other Time Lords left in time and space. After the Eleventh Doctor arrived in the bubble universe, he heard the distress calls on Nephew's translation sphere and thought this meant there were other living Time Lords besides Corsair. The Doctor was enraged when he found a cabinet filled with hypercubes which House had stolen from the dead Time Lords. (TV: The Doctor's Wife)

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

The New Dalek Paradigm and the Dalek Time Controller sent a hypercube to the Eleventh Doctor's TARDIS to lead him to the planet Gethria. From there, the Daleks manipulated the Doctor into leading them to the Cradle of the Gods, a monument which they planned to use to transform the Sunlight Worlds into copies of Skaro. Aided by Ollus, Sabel and Jenibeth Blakely, the Doctor set the Cradle to self-destruct and the Daleks abandoned the plan. (PROSE: The Dalek Generation)

Behind the scenes

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