The Boundary Volume of a Lattice Polytope
نویسندگان
چکیده
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 bd/2c 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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