# Lattice An

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Arranged to form a diagonal pattern of open spaces between the strips. An arrangement in space of isolated points in a regular pattern, showing the positions of atoms, molecules, or ions in the structure of a crystal.

Lattices as posets a partially ordered set (l,) is called a lattice if every pair of elements a and b in l has both a least upper bound (lu b) and a greatest lower bound (glb). The least upper bound is also called the join of a and b, denoted by a b. The greatest lower bound is also called the meet of a and b, and is denoted by ab.

## The ionic lattice Ionic compounds AQA GCSE Combined ..

A lattice is a nonempty set s with two binary operations, join and meet, denoted by and , respectively. In other words, to each pair of elements a and b in 5 there is associated a unique element a b in s, their join, and a unique element a b in 5, their meet.

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In geometry and group theory, a lattice in displaystyle mathbb r n is a subgroup of the additive group displaystyle mathbb r n which is isomorphic to the additive group displaystyle mathbb z n, and which spans the real vector space displaystyle mathbb r n. In other words, for any basis of displaystyle mathbb r n, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice.

The ions have a regular, repeating arrangement called an ionic lattice.

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In geometry and group theory, a lattice in displaystyle mathbb r n is a subgroup of the additive group displaystyle mathbb r n which is isomorphic to the additive group displaystyle mathbb z n, and which spans the real vector space displaystyle mathbb r n. In other words, for any basis of displaystyle mathbb r n, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice. A lattice may be viewed as a regular tiling of a space by a primitive cell.