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.
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A.M.S.
Electronic Research Announcements of the American Mathematical Society
Semidefinite programming and combinatorial optimization , Spinoza prijs Lex Schrijver
Networks and Optimization

Dutour Sikirić, M., Schuermann, A., & Vallentin, F. (2007). Classification of eight dimensional perfect forms. Electronic Research Announcements of the American Mathematical Society, 13, 21–32.