[math-fun] Spherohedron???

2D: consider the polygon whose vertices are lattice points that have distance exactly sqrt(N) from the origin, where N is an integer. (They don't exist for all N.) ditto for 3D, 4D, etc. (In 4D, these should exist for every N.) ... Do these things have a name?? --- I was thinking about a problem where you take a large sphere about the origin & shrink it down & watch the lattice points on its surface move about.