John Conway and I studied various lattices intermediate between the fcc and the bcc back in 1992. Our favorite is the "mcc" lattice, which is described in papers #177 and #291 on my pub. list on my home page (see below). The lattice with kissing number 10 that you describe has, I believe, Gram matrix [4 -1 -1 / -1 4 -2 / -1 -2 4]. We called it the "acc" lattice. It was described by Fields in 1980. Its theta series is in A028967 in the OEIS. Neil On Tue, Feb 5, 2013 at 5:50 PM, Warren Smith <warren.wds@gmail.com> wrote:
The new lattice appears to be "integral," that is, all interpoint distances, when squared, are integer multiples of the nearest-neighbor squared distance.
(Though I admit, I only checked a few distances.)
Can you compute its "theta series"?
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-- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com