I'd recommend reading Sphere Packings, Lattices and Groups, by J. H. Conway and N. J. A. Sloane. That lists all of the known interesting lattices in small numbers of dimensions. Sincerely, Adam P. Goucher
Can anyone please point me to any article or book that addresses the question of what are the maximal finite subgroups of GL(n,Z) ?
What I'm ultimately interested in is this:
Which n-dimensional lattices L (in R^n) have a maximal automorphism group Aut(L) -- maximal as a subgroup of O(n) ?
(Aut(L) here is the group of isometries of R^n that fix the origin and take L onto L.)
E.g., in 2D these are the square and triangular lattices. In 3D I think these are the cubic, bcc and fcc lattices. I don't know the answer for higher dimensions.
Thanks,
Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun