All the quantum numbers that define a particle can be looked at as values within a dimension. It's possible that some are redundant in the standard model, or not the greatest basis.

The simplest states that exist in the largest dimensions we know of are the position/spacetime states. String theory posits that these little tiny looped strings of matter, exist in dimensions that are on the verge of a planck length. They just loop around. If you went from where you are, to where I am, you'll have looped around those tiny string dimensions a crap ton of times.