Weighted projective spaces and reflexive simplices

 We derive a classification algorithm for reflexive simplices in arbitrary fixed dimension. It is based on the assignment of a weight Q ? ℕ ⁿ⁺¹ to an integral n-simplex, the construction, up to an isomorphism, of all simplices with given weight Q, and the characterization in terms of the weight as to when a simplex with reduced weight is reflexive. This also yields a convex-geometric reproof of the characterization in terms of weights for weighted projective spaces to have at most Gorenstein singularities. Received: 30 March 1999 / Revised version: 18 October 2001