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THE BOUNDARY VOLUME OF A LATTICE POLYTOPE
Published online by Cambridge University Press: 26 September 2011
Abstract
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 formulas for the f-vector of a smooth polytope in dimensions three, four, and five. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 84 - 104
- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2011
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