The Hypercube is one of the three 4D objects. It is also needed to unlock the Nova Flamethrower.
How to obtain:
1: When you have high enough intelligence (375+) you can challenge, and defeat, Chess Master Chase (in the U of S) to a chess match. When you accept, he will give you a Hypercube. (Note that you don't actually have to play him in chess).
2: In the police station there is an inmate called the 'Nigerian Prince'. He will ask for a $10,000 bail to get out of jail. Give him the $10,000 and he will reward you with bad karma and a Hypercube.
3: Find The Dimensional Drifter and buy the Hypercube from him for $100,000.