Maximilian Kreuzer, Benjamin Nill
Abstract
Abstract We obtain 866 isomorphism classes of five-dimensional nonsingular toric Fano varieties using a computer program and the database of four-dimensional reflexive polytopes. The algorithm is based on the existence of facets of Fano polytopes having small integral distance from any vertex.
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Abstract We obtain 866 isomorphism classes of five-dimensional nonsingular toric Fano varieties using a computer program and the database of four-dimensional reflexive polytopes. The algorithm is based on the existence of facets of Fano polytopes having small integral distance from any vertex.
Key concepts: Polytope, Fano plane, Mathematics, Invertible matrix, Isomorphism (crystallography), Vertex (graph theory), Combinatorics, Pure mathematics