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The boundary volume of a lattice polytope


Alexander M. Kasprzyk


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 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.


Hegedüs, G., & Kasprzyk, A. M. (2011). The boundary volume of a lattice polytope. Bulletin of the Australian Mathematical Society, 85(1),

Journal Article Type Article
Publication Date Sep 26, 2011
Deposit Date Nov 12, 2015
Publicly Available Date Nov 12, 2015
Journal Bulletin of the Australian Mathematical Society
Print ISSN 0004-9727
Electronic ISSN 1755-1633
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 85
Issue 1
Keywords Lattice polytope, Boundary volume, Reflexive polytope, Order polytope, Birkhoff polytope
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Additional Information Copyright Australian Mathematical Society 2011


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