The Three Great Treasures of Generios were demanded as tribute by the Cylinder from Potikol, the leader of Generios 1. The treasures were the Shelves of Infinity, Mentos and the largest diamond in existence.
Shelves of Infinity
The Shelves of Infinity, also known as Unit Zed-X4-one-9, was a piece of furniture created by the Assemblers on Generios 8. It was said to be their greatest achievement.
What was so special about the Shelves was that the pieces (which kept appearing and disappearing) were able to exist in multiple dimensions. The instructions also kept getting longer.
Melanie Bush and Banto Zame were able to obtain the Shelves of Infinity by tricking the Assemblers into thinking they had finished building them.
Mentos
Mentos or the Mentos Devise was computer that contained all the knowledge of the known universe by having a team of electronic research devises located in a shadow universe tell him what he needed to know. He appeared as a computer projection located on Generios 14.
Mentos was created by one of the societies of the planet. Two warring fractions fought and destroyed each other to get to him.
He was placed on the game show The Feeblest Contestant (a parody of The Weakest Link) as a gimmick to show off its intelligence. He was the only contestant on the show for 33,000 years, having been programmed to answer any question put to him. The only way to stop the game was for Mentos to answer a question incorrectly or for someone to figure out the code to turn him off, which was lost with his creators who died thousands of years before.
The Sixth Doctor and Sally-Anne Stubbins were able to obtain Mentos by asking him a question he was unable to answer.
Largest diamond in existence
The largest diamond in existence was located on Generios 15. The Doctor's TARDIS landed there with the Sixth Doctor, Melanie Bush, Banto Zame and Sally-Anne Stubbins.
It was guarded by a Spraxis Jelloid who was under a 50 million year, non-negotiable contract.
The diamond was held in place by a giant force field which the Jelloid could shut off.
The group was able to obtain the diamond merely by asking the Jelloid to turn off the force field and letting the Doctor take it. (AUDIO: The One Doctor)