Square Bravais lattice ($\Lambda =\ell R{\mathbb{Z}}^2$)

A two-dimensional Bravais lattice with perpendicular primitive vectors of the same length $\ell$. An orthogonal matrix $R$ gives its orientation, and its primitive area is ${\ell }^2$. Its nearest-neighbor graph is a square lattice; the set of crystal translations and the graph with chosen adjacency are related but distinct objects.