On Lattices Equivalent To Their Duals Original Research Article

A lattice is called isodual if it is geometrically congruent to its dual. We show that the densest three-dimensional isodual lattice is the "mean centered-cuboidal" lattice, a lattice which is in a sense the mean of the face-centered and body-centered cubic lattices. This lattice is also the most economical three-dimensional isodual covering. We give a number of other dense isodual lattices in imagen, n ≤ 24.