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.
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.
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