- (MATH) A periodic arrangement
of points such as the vertices of a tiling
of space by cubes or the positions of atoms in a crystal. More technically,
a discrete Abelian subgroup of an n-dimensional vector
space which not contained in an (n-1)-dimensional vector
space. Lattices play a central role in the theory of Lie
groups, in number theory,
in error-correcting codes, and many other areas of mathematics. A lattice
is often, but not always, distinguished from a graph
in that a lattice is a graph with a regular structure.
- (CHEMISTRY) A regular network
of fixed points about which molecules,
atoms, or ions
vibrate in a crystal.