Enumeration of Lattice 3-Polytopes by Their Number of Lattice Points

@article{Blanco2018EnumerationOL,
  title={Enumeration of Lattice 3-Polytopes by Their Number of Lattice Points},
  author={M. Blanco and F. Santos},
  journal={Discrete & Computational Geometry},
  year={2018},
  volume={60},
  pages={756-800}
}
  • M. Blanco, F. Santos
  • Published 2018
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • We develop a procedure for the complete computational enumeration of lattice 3-polytopes of width larger than one, of which there are finitely many for each given number of lattice points. We also implement an algorithm for doing this and enumerate those with at most 11 lattice points (there are 216,453 of them). In order to achieve this we prove that if P is a lattice 3-polytope of width larger than one and with at least seven lattice points then it fits in one of three categories that we call… CONTINUE READING
    Enumeration of Lattice Polytopes by Their Volume
    2
    Non-spanning lattice 3-polytopes
    4
    Elementary moves on lattice polytopes
    2
    Classification of lattice polytopes with small volumes
    7
    The diameter of lattice zonotopes.
    2
    C O ] 1 2 M ay 2 01 9 THE DIAMETER OF LATTICE ZONOTOPES
    The pyramidal growth

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 15 REFERENCES
    Lattice 3-Polytopes with Few Lattice Points
    17
    Lattice 3-Polytopes with Six Lattice Points
    10
    Minkowski Length of 3D Lattice Polytopes
    9
    Lattice Polytopes with Distinct Pair-Sums
    9
    Three-dimensional lattice polytopes with two interior lattice points
    11
    Lectures on Polytopes
    2950
    Toric Surface Codes and Minkowski Length of Polygons
    32
    Integral Polyhedra in Three Space
    20
    Minimal volume K-point lattice D-simplices
    6
    Quantum Jumps of Normal Polytopes
    5