Thanks very much, Neil, for the pointer to your paper. Now I will need to figure out which if any of these "maximally symmetric" lattices (besides A*_2 and A*_3) have Voronoi tessellations with vertex figures that are simplices. Any further pointers to where this information might be found will be greatly appreciated. -Dan On 2012-07-28, at 12:39 PM, Dan Asimov wrote:
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.