I mean the same thing that a "squared square" usually means: a tiling of a square torus by squares of distinct sizes. Ideally this would be without any 4-way intersections: _|_ | (and I don't want to exclude the possibility of such tilings having sides that are not parallel to the "sides" of the square torus, in case any such may exist). But even forgetting oblique tilings, the possibility exists that if there are such things as squared square tori, they may beat the records for squared squares, since they involve fewer constraints. —Dan ----- Dan, do you mean to exclude the near-trivial family related to the Pythagorean tiling? Any two squares tile a square torus. I don't know of any *other* examples, though. On Thu, Jul 23, 2020 at 8:19 PM Dan Asimov <dasimov@earthlink.net> wrote:
Has anyone ever found a squared square torus that wasn't a squared square?