I see a possible pattern where adding a dimension increases functionality....
eg: gears to spheres
One example I've thought of is the chemist who came up with the benzene ring. He was trying to figure out how all the bonds could work together as advertised, and had an inspiration that they could be in a ring rather than a straight line.
There are wonderful molecules called "fullerenes" (the most famous of which
is actually called BuckminsterFullerene?), consisting of lots of carbon atoms
in a geodesic-dome sort of shape. BuckminsterFullerene? itself is the
lowest-energy configuration possible for 60 carbon atoms. (These molecules
are named in honour of BuckminsterFuller, who worked on geodesic domes
and recognised their great stability, though he didn't anticipate the
existence of the molecules that bear his name.) [DeleteMe: this paragraph
has been considerably changed from Shae's original, so he may wish
to disavow it.]
--ShaeErissonThe next dimension might be a bit harder.
I don't think so... My reasoning is that you just think in the higher dimensions, you don't have to have them in front of you. I think this is a pattern to suggest how you can shift your paradigm more than anything else.
See also CritiqueOfUseCases for a small discussion on dimensionality of software system models.