## Bravais lattice |

in

andgeometry , acrystallography **bravais lattice**, named after (auguste bravais 1850 ),^{[1]}is an infinite array of discrete points generated by a set of operations described in three dimensional space by:discrete translation where

*n*are any integers and_{i}**a**_{i}are*primitive vectors*which lie in different directions (not necessarily mutually perpendicular) and span the lattice. this discrete set of vectors must be closed under vector addition and subtraction. for any choice of position vector**r**, the lattice looks exactly the same.when the discrete points are

,atoms , orions strings ofpolymer , the bravais lattice concept is used to formally define asolid matter *crystalline arrangement*and its (finite) frontiers. a is made up of a periodic arrangement of one or more atoms (thecrystal *basis*, or*motif*) repeated at each lattice point. consequently, the crystal looks the same when viewed from any equivalent lattice point, namely those separated by the translation of one unit cell.two bravais lattices are often considered equivalent if they have isomorphic symmetry groups. in this sense, there are 14 possible bravais lattices in three-dimensional space. the 14 possible symmetry groups of bravais lattices are 14 of the 230

. in the context of the space group classification, the bravais lattices are also called bravais classes, bravais arithmetic classes, or bravais flocks.space groups ^{[2]}- in 2 dimensions
- in 3 dimensions
- in 4 dimensions
- see also
- references
- further reading
- external links

In **Bravais lattice**, named after ^{[1]} is an infinite array of discrete points generated by a set of

where *n _{i}* are any integers and

When the discrete points are *crystalline arrangement* and its (finite) frontiers. A *basis*, or *motif*) repeated at each lattice point. Consequently, the crystal looks the same when viewed from any equivalent lattice point, namely those separated by the translation of one unit cell.

Two Bravais lattices are often considered equivalent if they have isomorphic symmetry groups. In this sense, there are 14 possible Bravais lattices in three-dimensional space. The 14 possible symmetry groups of Bravais lattices are 14 of the 230 ^{[2]}