Classification of eight dimensional perfect forms
نویسندگان
چکیده
In this paper, we classify the perfect lattices in dimension 8. There are 10916 of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here we describe algorithms making the classification possible.
منابع مشابه
On extreme forms in dimension 8
A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension 8 has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for ex...
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