Pessimal packing shapes

  title={Pessimal packing shapes},
  author={Yoav Kallus},
  journal={Geometry & Topology},
  • Yoav Kallus
  • Published 2015
  • Mathematics, Physics
  • Geometry & Topology
  • We address the question of which convex shapes, when packed as densely as possible under certain restrictions, fill the least space and leave the most empty space. In each different dimension and under each different set of restrictions, this question is expected to have a different answer or perhaps no answer at all. As the problem of identifying global minima in most cases appears to be beyond current reach, in this paper we focus on local minima. We review some known results and prove these… CONTINUE READING

    Figures and Tables from this paper.

    Paper Mentions

    The random packing density of nearly spherical particles.
    • 13
    • PDF
    Densest Local Structures of Uniaxial Ellipsoids
    • 5
    • PDF
    The Local Optimality of the Double Lattice Packing
    • 1
    • PDF


    Publications referenced by this paper.
    Double-lattice packings of convex bodies in the plane
    • 58
    • PDF
    The 3-ball is a local pessimum for packing
    • 11
    • PDF
    Research problems in discrete geometry
    • 693
    • PDF
    A New Packing Density Bound in 3-Space
    • 5
    • PDF
    Some basic properties of packing and covering constants
    • 9
    • PDF