  In this paper we prove that every H-type Lie algebra possesses a basis with
respect to which the structure constants are integers. Existence of such an
integral basis implies via the Mal'cev criterion that all simply connected
H-type Lie groups contain cocompact lattices. Since the Campbell-Hausdorff
formula is very simple for two-step nilpotent Lie groups we can actually avoid
invoking the Mal'cev criterion and exhibit our lattices in an explicit way. As
an application, we calculate the isoperimetric dimensions of H-type groups.
