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Abstract
We construct an algorithm for deducing all affinely nonequivalent types of \(L\)-polyhedra on n-lattices, where \(n \leqslant 5\). The computational part of the algorithm designed for calculations on a personal computer is based on the relationship between the geometry of lattices and the theory of hypermetric spaces. For the first time, a complete list of affine types (\(139\) types) of \(L\)-polyhedra on \(5 \)-lattices is obtained.
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