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Published online by Cambridge University Press:  26 September 2011

Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, A-4040 Linz, Austria (email:
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom (email:
For correspondence; e-mail:
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For a d-dimensional convex lattice polytope P, a formula for the boundary volume vol(∂P) is derived in terms of the number of boundary lattice points on the first ⌊d/2⌋ dilations of P. As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulas for the f-vector of a smooth polytope in dimensions three, four, and five. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.

Research Article
Copyright © Australian Mathematical Publishing Association Inc. 2011


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