Torus
Beginner
A grid of chips where each one talks to its neighbors, and the edges wrap around so the last chip in a row links back to the first.
Novice
A mesh (grid) of chips in two or three dimensions, with extra wraparound links joining opposite edges. Each chip connects only to its 4 (2D) or 6 (3D) nearest neighbors.
Expert
A -ary -cube: constant degree , diameter about , bisection bandwidth proportional to . Cheap to cable with short links, well suited to dimension-ordered collectives, but non-neighbor traffic takes multiple hops and shares links.