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
framework consisting of an ornamental design made of strips of wood or metal an arrangement of points or particles or objects in a regular periodic pattern in 2 or 3 dimensions
A lattice is a pattern or structure made of strips of wood or another material which cross over each other diagonally leaving holes in between. We were crawling along the narrow steel lattice of the bridge
An arrangement in space of isolated points in a regular pattern, which for example show the positions of atoms, molecules, or ions in the structure of a crystal
A surface representation that uses a rectangular array of points spaced at a constant sampling interval in the x and y directions relative to a common origin A lattice is stored as a grid, but differs in that it represents the value of the surface only at the mesh points of the lattice rather than the value of the cell area surrounding each mesh point
An orderly arrangement of atoms in a material, usually thought of as an infinite series of "cells" forming a "latticework" of atoms in 3-dimensions A thorough treatment of lattices and other materials issues can be found at the Visualizations in Materials Science WWW site
A discrete subgroup of the additive group of complex numbers Concretely, it is the set of all complex numbers of the form n + n for integers n, n and "periods" and (whose ratio is not a real number)
A surface representation that uses a rectangular array of mesh points spaced at a constant sampling interval in the x and y directions relative to a common origin A lattice is stored as a grid, but represents the value of the surface only at the mesh points rather than the value of the entire cell
In a periodic tiling, if you take any point in the pattern and apply to that point all the translations (but not any of the other 3 types of isometries), what results is a lattice for the pattern An example For periodic tilings, there are 5 types of lattices
A lattice is a collection of elements which form a pattern of bending and focusing magnets and defines the aperture of the magnets Typically an accelerator is composed of "cells" of magnets, or basic collections of magnets which repeat to create a periodic structure The lattice functions are functions which depend only on the periodic structure and the magnets used and which describe the basic parameters of the beams trajectory and size
a graphlike configuration where each axis is devoted to tones generated by a specific prime number; a two-dimensional lattice (i e , on a page) is confined to a tuning system using two primes A lattice of tones combines the graph principle with staff notation by skewing the direction of both axes A lattice of twelve notes refers to the twelve most simply derived ratios; an extended lattice includes indefinitely more notes; a chord lattice abandons the staff notation and shows the major and minor triads by chord symbols only; in a key lattice, the symbols stand for keys
is an abstract base class which presents an interface to a finite-volume, linear, rectangular, or hyper-rectangular structure The Lattice is fundamentally described by its shape
Space lattice Lattice lines and lattice planes are lines and planes chosen so as to pass through collinear lattice points, and non-collinear lattice points, respectively