Primitive and Centered Cells

The only tilings with rhombic lattices are those of type cm and cmm.

cm cmm

The reflection axes (dotted lines below) for these tilings are not  in the same direction as rhombus' edges (the solid lines). 

For this reason (although for all I know there may be others), centered cells are chosen for tilings with symmetry groups cm and cmm.  To get a centered cell, draw a rectangle with lattice points at the vertices and a lattice point at the center.

A centered cell has twice the area of a primitive cell

Tiling Definitions  Identifying the 17 Plane Symmetry groups