If $\nabla_{Y}$ defines an integral affine structure on $Y$ with the covariantly constant lattice $(TY)^{{\bf Z}}$ then $\nabla_{Y}^{\vee}$ defines an integral affine structure on $Y^{\vee}$ such that for all $x\in Y^{\vee}=Y$ the lattice $(T_{x}Y^{\vee})^{{\bf Z}}$ is dual to $(T_{x}Y)^{{\bf Z}}$ with respect to the Riemannian metric $g_{Y}$ on $Y$.