Two-dimensional Bravais lattice ($\Lambda =\mathbb{Z}{\mathbf{a}}_1+\mathbb{Z}{\mathbf{a}}_2$)

The set $\{n_1{\mathbf{a}}_1+n_2{\mathbf{a}}_2:n_1,n_2\in \mathbb{Z}\}$ for two independent planar translation vectors. Its primitive-cell area is $|\det ({\mathbf{a}}_1,{\mathbf{a}}_2)|$.

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.

A lattice represented by a rectangular conventional cell with corner points and one center point. For conventional sides $2a,2b$, primitive vectors can be $(a,b)$ and $(-a,b)$. The special case $a=b$ is a square lattice with a rotated primitive basis.