The boundary volume of a lattice polytope

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.

21 pages; subsumes arXiv:1002.1908 [math.CO]; to appear in the Bulletin of the Australian Mathematical Society

References in corpus (2)

• An algorithm for the classification of smooth Fano polytopes
• A note on palindromic $\delta$-vectors for certain rational polytopes

Cited by in corpus (2)

• Reverse lexicographic squarefree initial ideals and Gorenstein Fano polytopes
• Roots of Ehrhart Polynomials of Smooth Fano Polytopes