I have encountered a theorem stating that a perfect quadratic form is equivalent to a quadratic form lying on some extreme ray of the Minkowski reduction domain. Now I am wondering whether a perfect form (in the Ryshkov polyhedron) is always equivalent (unimodular equivalence) to a form that is a vertex of the Minkowski domain? Are there perfect forms, when after being Minkowski reduced, correspond to a form in the Minkowski domain that is not a vertex in the domain? Thanks in advance.
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no, this cannot happen. |
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