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