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The square torus is the quotient of the plane by the integer lattice.

A benzenoid is a fusene that is a subgraph of the regular hexagonal lattice (i.e., a simply connected polyhex). The numbers of n-hexagon benzenoids for n=1, 2, ... are 1, 1, ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

The automorphism group Co_1 of the Leech lattice modulo a center of order two is called "the" Conway group. There are 15 exceptional conjugacy classes of the Conway group. ...

For a given point lattice, some number of points will be within distance d of the origin. A Waterman polyhedron is the convex hull of these points. A progression of Waterman ...

A lattice reduction algorithm, named after discoverers Lenstra, Lenstra, and Lovasz (1982), that produces a lattice basis of "short" vectors. It was noticed by Lenstra et al. ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

While the Catalan numbers are the number of p-good paths from (n,n) to (0,0) which do not cross the diagonal line, the super Catalan numbers count the number of lattice paths ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...