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 First Doctor collected his when he worked for the Bureau of Possible Events, but left it 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. (PROSE: 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, 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 poor choice for the Doctor; it led to his Exile on Earth as the Third Doctor and the separation from his companions Jamie McCrimmon and Zoe Heriot. (TV: The War Games)

Hundreds of Time Lords, stranded in the bubble universe by House, used hypercubes to send distress calls. However, none of them remained alive by the time other Time Lords arrived; House killed them for parts to repair Auntie and Uncle. This produced TARDISes to feed House for five thousand years. The last Time Lord to arrive on House was the Doctor's good friend the Corsair. He recorded his hypercube, but was killed before he could send it. The Corsair's hypercube was sent into the main universe and found the Doctor's TARDIS because there were no other Time Lords left in time and space. After the 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. All the Doctor found was a cabinet filled with hypercubes 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) Being manipulated and thus putting millions of lives in danger, however, caused the Doctor to retire. (TV: The Great Detective)

Behind the scenes

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