Heesch Number

The Heesch number of a closed plane figure is the maximum number of times that figure can be completely surrounded bycopies of itself. The determination of the maximum possible (finite) Heesch number is known as Heesch's Problem. The Heesch number of a Triangle, Quadrilateral, regular Hexagon, or any other shape that canTile or Tessellate the plane, is infinity. Conversely, any shape with infiniteHeesch number must tile the plane (Eppstein). The largest known (finite) Heesch number is 3, and corresponds to a tileinvented by R. Ammann (Senechal 1995).

References

Eppstein, D. ``Heesch's Problem.'' http://www.ics.uci.edu/~eppstein/junkyard/heesch/.

Fontaine, A. ``An Infinite Number of Plane Figures with Heesch Number Two.'' J. Comb. Th. A 57, 151-156, 1991.

Senechal, M. Quasicrystals and Geometry. New York: Cambridge University Press, 1995.

• Liouville's Rational Approximation Theorem
• Liouville's Sphere-Preserving Theorem
• Lipschitz Condition
• Lipschitz Function
• Lipschitz's Integral
• Lissajous Curve
• Lissajous Figure
• List
• Lituus
• Lituus Inverse Curve
• LLL Algorithm
• Ln
• Lobachevsky-Bolyai-Gauss Geometry
• Lobachevsky's Formula
• Lobatto Quadrature
• Lobster
• Local Cell
• Local Degree
• Local Density
• Local Density Conjecture
• Local Extremum
• Local Field
• Local-Global Principle
• Local Group Theory
• Locally Convex Space