A simplicial lattice polytope containing the origin in the interior is called a smooth Fano polytope, if the vertices of every facet is a basis of the lattice. The study of smooth Fano polytopes is motivated by their connection to toric varieties.
The thesis concerns the classification of smooth Fano polytopes up to isomorphism.
A smooth Fano d-polytope can have at most 3d vertices. In case of 3d vertices an explicit classification is known. The thesis contains the classification in case of 3d−1 vertices.
Classifications of smooth Fano d-polytopes for fixed d exist only for d≤5. In the thesis an algorithm for the classification of smooth Fano d-polytopes for any given d is presented. The algorithm has been implemented and used to obtain the complete classification for d≤8.