  An n-dimensional simplex \Delta in \R^n is called empty lattice simplex if
\Delta \cap\Z^n is exactly the set of vertices of \Delta . A theorem of G. K.
White shows that if n=3 then any empty lattice simplex \Delta \subset\R^3 is
isomorphic up to an unimodular affine linear transformation to a lattice
tetrahedron whose all vertices have third coordinate 0 or 1. In this paper we
prove a generalization of this theorem for an arbitrary odd dimension n=2d-1
which in some form was conjectured by Seb\H{o} and Borisov. This result implies
a classification of all 2d-dimensional isolated Gorenstein cyclic quotient
singularities with minimal log-discrepancy at least d.
