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translation lattice

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  • 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

  • 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

  • Niemeier lattice — In mathematics, a Niemeier lattice is one of the 24 positive definite even unimodular lattices of rank 24, which were classified by Hans Volker Niemeier (1973). Venkov (1978) gave a simplified proof of the classification. Witt (1941) has a… …   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

  • One-dimensional symmetry group — A one dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x. The 1D isometries map x to x + a and to a − x.… …   Wikipedia

  • Crystal system — Diamond crystal structure consists of face centered cubic lattice. In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals.… …   Wikipedia

  • Close-packing of spheres — hcp and fcc close packing of spheres In geometry, close packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the… …   Wikipedia

  • Point groups in two dimensions — In geometry, a point group in two dimensions is an isometry group in two dimensions that leaves the origin fixed, or correspondingly, an isometry group of a circle. It is a subgroup of the orthogonal group O(2), the group of all isometries which… …   Wikipedia

  • Permutohedron — In mathematics, the permutohedron of order n is an ( n − 1) dimensional polytope embedded in an n dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3, ..., n ).Examples* Order 1: A single point …   Wikipedia

  • Space group — In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains. In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered… …   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


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