2006/09/28 by Nicolas Ressayre, Ressayre, Nicolas, Pierre-Louis Montagard +1
Engineering · Materials Science · Mathematics · #Advanced Materials and Mechanics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Point processes and geometric inequalities #Quasicrystal Structures and Properties #math.AG #math.CO
paper · pdf · doi:10.48550/arxiv.math/0609809
14 pages, 1 Figure, 1 Table
arxiv created 2006/09/28 · openalex publication_date 2006/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a lattice in a real finite dimensional vector space. Here, we are interested in the lattice polytopes, that is the convex hulls of finite subsets of the lattice. Consider the group G of the affine real transformations which map the lattice onto itself. Replacing the group of euclidean motions by the group G one can define the notion of regular lattice polytopes. More precisely, a lattice polytope is said to be regular if the subgroup of G which preserves the polytope acts transitively on the set of its complete flags. Recently, Karpenkov obtained a classification of the regular lattice polytopes. Here we obtain this classification by a more conceptual method. Another difference is that Karpenkov uses in an essential way the classification of the euclidean regular polytopes, but we don't.