Translational symmetry — In geometry, a translation slides an object by a vector a: Ta(p) = p + a.In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation. Discrete translational symmetry is invariance … Wikipedia
Lattice (group) — A lattice in the Euclidean plane. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn … Wikipedia
Lattice (mathematics) — In mathematics, the term lattice can mean:* A partially ordered set (poset) in which any two elements have a supremum and an infimum mdash;see lattice (order). The Hasse diagrams of these posets look (in some simple cases) like the lattices of… … Wikipedia
Hexagonal lattice — The hexagonal lattice or equilateral triangular lattice is one of the five 2D lattice types.Three nearby points form an equilateral triangle. In images four orientations of such a triangle are by far the most common. They can conveniently be… … Wikipedia
Square lattice — In mathematics, the square lattice is one of the five two dimensional lattice types. It is the two dimensional version of the integer lattice.Two orientations of an image of the lattice are by far the most common. They can conveniently be… … Wikipedia
Bravais lattice — In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, [cite journal | last = Aroyo | first = Mois I. | coauthors = Ulrich Müller and Hans Wondratschek | title = Historical Introduction | journal = International Tables… … Wikipedia
Rotational symmetry — Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the … Wikipedia
Thermodynamic temperature — is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an “absolute” scale because it is the measure of the fundamental property underlying temperature: its null or zero point … Wikipedia
Wallpaper group — A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and… … Wikipedia
Symmetry combinations — This article discusses various symmetry combinations.In 2D, mirror image symmetry in combination with n fold rotational symmetry, with the center of rotational symmetry on the line of symmetry, implies mirror image symmetry with respect to lines… … Wikipedia
Crystal structure — In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice… … Wikipedia