certainly the n-dim lattice "integer coords with even sum" is the D_n lattice. In 2-D it is the checkerboard in 3-D it is the face-centered cubic lattice there are two tilings that go with it, the main one being the decomposition of space into the Voronoi cells around the lattice points the other one is the dual tiling, into Delaunay regions, which are centered at the holes in the lattice (meaning the points that are locally maximally distant from the lattice points). Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Fri, Sep 21, 2018 at 10:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Errrm. Either I need to think a bit more about firming my argument up, or I have a touch of incipient MFA syndrome ...
Watch this space, folks.
WFL
On 9/21/18, Dan Asimov <dasimov@earthlink.net> wrote:
That sounds like the checkerboard lattice D_n in n-space,
D_n = {(x_1, ..., x_n) in Z^n | x_1 + ... + x_n == 0 mod 2}
—Dan
----- the unit-sphere packing where centres have evenly many odd integer Cartesian components. -----
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