## Lattice PointsContains solved and unsolved problems concerning lattice points, especially geometric, number theoretic, combinatorial, and analytic results, theories, and problems related to lattice points. Emphasis is on the geometry of numbers. Provides extensive comments on each problem, consisting mostly of heuristic arguments and intuitive descriptions. There are only a few proofs. Annotation copyrighted by Book News, Inc., Portland, OR |

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### Contents

Equidissectable polytopes | 1 |

Lattice polytopes lattice point enumerators and a glimpse of algebraic geometry | 6 |

Minkowskis fundamental theorem and some of its relatives | 14 |

Copyright | |

17 other sections not shown

### Common terms and phrases

Akad algorithm Amer Math applications balls Baranovskii bound boundary called cell codes combinatorial compact concept congruent conjecture consider consisting constant contains convex body corresponding covering crystal defined denote density determinant dimensions domain edges equal equivalent example exist extreme Fejes Tóth figure finite fundamental theorem geometry geometry of numbers give given graph Gruber holds inequality integer interesting interior intersection lattice covering lattice packing lattice points least linear London Math Soc measure method Minkowski multiplicity Nauk Note obtained origin packing and covering particular plane polygons polytopes positive positive quadratic forms possible precisely problem Proc proof proper properties proved provides reduced refer remarks respectively says sequence shows solution space space groups space-group spheres square star subset suitable symmetric theory tiling translates types unit University values vertices volume Voronoi