Classification of lattice-regular lattice convex polytopes
نویسندگان
چکیده
منابع مشابه
2 00 6 Classification of Lattice - Regular Lattice Convex Polytopes
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In this paper for any dimension n we give a complete description of lattice convex polytopes in R that are regular with respect to the group of affine transformations preserving the lattice.
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We show by a direct construction that there are at least exp{cV (d−1)/(d+1)} convex lattice polytopes in R of volume V that are different in the sense that none of them can be carried to an other one by a lattice preserving affine transformation. This is achieved by considering the family Pd(r) (to be defined in the text) of convex lattice polytopes whose volumes are between 0 and r/d!. Namely ...
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submitted at the Oberwolfach Conference “Combinatorial Convexity and Algebraic Geometry” 26.10–01.11, 1997 Throughout, we fix the notation M := Z and MR := R . Given convex lattice polytopes P, P ′ ⊂ MR, we have (M ∩ P ) + (M ∩ P ) ⊂ M ∩ (P + P ), where P + P ′ is the Minkowski sum of P and P , while the left hand side means {m+m | m ∈ M ∩ P,m ∈ M ∩ P }. Problem 1 For convex lattice polytopes P...
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ژورنال
عنوان ژورنال: Functional Analysis and Other Mathematics
سال: 2007
ISSN: 1991-0061,1863-7914
DOI: 10.1007/s11853-007-0002-z