The boundary volume of a lattice polytope
Hegedüs, Gábor and Kasprzyk, Alexander M. (2011) The boundary volume of a lattice polytope. Bulletin of the Australian Mathematical Society, 85 (1). pp. 84-104. ISSN 1755-1633
Official URL: http://dx.doi.org/10.1017/S0004972711002577
For a d-dimensional convex lattice polytope P, a formula for the boundary volume vol(δP) 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 formulae for the f-vector of a smooth polytope in dimensions 3, 4, and 5. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.
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