Translation lattice
= Translation lattice
{title2=$\Lambda=\mathbb Zv_1+\cdots+\mathbb Zv_r$}
A translation lattice is the additive group generated by linearly independent vectors $v_1,\ldots,v_r$ in a Euclidean space. It defines a <discrete subgroup> of <translations>. A full-rank translation lattice has a compact parallelepiped as a fundamental region and therefore a <cocompact group action>. This geometric usage is distinct from an order-theoretic lattice.