2007•arXiv (Cornell University)Open access

An algorithm for the classification of smooth Fano polytopes

Mikkel Øbro

Abstract

We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.

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Key concepts: Polytope, Fano plane, Isomorphism (crystallography), Integer (computer science), Combinatorics, Algorithm, Mathematics, Polytope model