There are at two other differences between your notion and Waterman's. One is that his points are in a face-centered cubic lattice, not in your body-centered cubic. The other is that Waterman includes all points at the critical distance *and closer*. On Thu, Aug 28, 2014 at 5:41 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Thanks! My 3D versions are a subset of "generalized Waterman polyhedra".
Here's something from OEIS:
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.
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