Mathematica makes some attempts to project hyper-dimensions onto 2-space with the Hypercube command. Likewise some attempts at tying them to our universe are mentioned at http://ctp.berkeley.edu/extraD.html .
The MRB constant from infinite-dimensional space is feebly described at http://marvinrayburns.com/ThegeometryV12.pdf . It is my theory that the like the MRB constant the universe, under inflation, started in an infinite number of space dimensions. And the universe almost instantly lost, as far as our sensory realm is concerned, all but the few we enjoy today.