  The simplest toroidally compactified string theories exhibit a duality
between large and small radii: compactification on a circle, for example, is
invariant under R goes to 1/R. Compactification on more general Lorentzian
lattices (i.e. toroidal compactification in the presence of background metric,
antisymmetric tensor, and gauge fields) yields theories for which large-small
invariance is not so simple. Here an equivalence is demonstrated between large
and small geometries for all toroidal compactifications. By repeatedly
transforming the momentum mode corresponding to the smallest winding length to
another mode on the lattice, it is possible to increase the volume to exceed a
finite lower bound.
