smooth polytope
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2011 ◽  
Vol 85 (1) ◽  
pp. 84-104
Author(s):  
GÁBOR HEGEDÜS ◽  
ALEXANDER M. KASPRZYK

AbstractFor 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.


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