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In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.
This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1. The E 8 lattice and the Leech lattice are two famous examples.
The seven lattice systems and their Bravais lattices in three dimensions. In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (), [1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice , or grid lattice.
Lattice (group), for the case where M is a Z-module embedded in a vector space V over the field of real numbers R, and the Euclidean metric is used to describe the lattice structure References [ edit ]
Archimedean lattices. Add languages. Add links. Article; Talk; English. Read; Edit; View history; Tools. ... List of Euclidean uniform tilings#Convex uniform tilings ...
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