Thanks! My 3D versions are a subset of "generalized Waterman polyhedra". Here's something from OEIS: http://oeis.org/A119870 However, there seem to be small discrepancies: this sequence talks about sqrt(2N) instead of sqrt(N). The polyhedra that I'm interested in are convex hulls of the lattice points at distance exactly sqrt(N) from the origin. I'd like to know the name of this particular subset (if it has a name). At 12:48 PM 8/28/2014, Allan Wechsler wrote:
In three dimensions, these are something like the Waterman polyhedra. Try googling for that.
On Thu, Aug 28, 2014 at 3:01 PM, Henry Baker <hbaker1@pipeline.com> wrote:
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.