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arXiv · 1002.2815

The boundary volume of a lattice polytope

Gábor Hegedüs·Alexander M. Kasprzyk
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Abstract

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ 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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BibTeXRIS

Gábor Hegedüs, Alexander M. Kasprzyk. 2011-05-30. The boundary volume of a lattice polytope. https://doi.org/10.1017/s0004972711002577

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