Representation theory and polytopes

This cumulative habilitation thesis contains several papers concerning applications of the representation theory of finite groups to polytopes and their symmetries, and in particular, orbit polytopes (also known as vertex-transitive polytopes). The topics treated include affine symmetry groups of orbit polytopes, lattice-free orbit polytopes, the combinatorial symmetry group of the Birkhoff polytope and realizations of abstract regular polytopes.Diese kumulative Habilitationsschrift enthält verschiedene Arbeiten über Anwendungen der Darstellungstheorie endlicher Gruppen auf Polytope und ihre Symmetrien, insbesondere Orbit-Polytope (auch eckentransitive Polytope genannt). Behandelt werden unter anderem affine Symmetriegruppen von Orbit-Polytopen, gitterfreie Orbit-Polytope, die kombinatorische Symmetriegruppe des Birkhoff-Polytops und Realisierungen abstrakt-regulärer Polytope