Erm, I could be wrong but wouldn't the icosahedron be the maximum "evenly spaced" set of people on the surface of a sphere (that weren't all confined to a great circle)? Lots of regular polygons, rather fewer regular polyhedra.

(Of course if we make the jump to a 4D sphere we can put 600 people into the largest regular polytope, the hexacosichoron. http://en.wikipedia.org/wiki/Convex_regular_4-polytope)

EDIT: I am wrong, it'd only take a uniform polyhedron, not a regular one. E.g. http://en.wikipedia.org/wiki/Icosidodecahedron