Tom Karzes wrote: ----- I really just want a single shrunken version of the object. Adding reflection is trivial (just negate x or y), so there's no need to throw reflected solutions into the mix. Once a reference solution is found, the solution set can be quadrupled by rotating by multiples of 90 degrees, and doubled by adding reflection if desired, so there's no reason to use a reflected solution as the reference solution. ----- The solution set can indeed be multiplied by four via 90º rotations ... or multiplied by infinity via adding an arbitrary integer vector. By the way, this is a very interesting problem (which I haven't tried to solve yet)! Tom's question also suggests the corresponding problem for the triangular lattice Z[w] = {P(w) | P(x) is an integer polynomial}. where w = exp(2πi/3). —Dan