  Regular integer lattices are characterized by k unit vectors that build up
their generator matrices. These have rank k for D-lattices, and are
rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside
hypercubes centered at the origin for all three types, as if classified by
maximum infinity norm in the host lattice. The results assume polynomial format
as a function of the hypercube edge length.
