Discrete & Computational Geometry

, Volume 52, Issue 2, pp 153–194

Smooth Fano Polytopes with Many Vertices



The \(d\)-dimensional simplicial, terminal, and reflexive polytopes with at least \(3d-2\) vertices are classified. In particular, it turns out that all of them are smooth Fano polytopes. This improves on previous results of Casagrande (Ann Inst Fourier (Grenoble) 56(1):121–130, 2006) and Øbro (Manuscr Math 125(1): 69–79, 2008). Smooth Fano polytopes play a role in algebraic geometry and mathematical physics.


Toric Fano varieties Lattice polytopes Terminal polytopes  Smooth polytopes 

Mathematics Subject Classification

52B20 14M25 14J45 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Inst. MathematikTU BerlinBerlinGermany
  2. 2.FB MathematikTU DarmstadtDarmstadtGermany

Personalised recommendations