10.18453/rosdok_id00001330 Rehn, Thomas Thomas Rehn http://d-nb.info/gnd/1049767993 Universität Rostock 2014 510 Mathematics 2014 en http://purl.uni-rostock.de/rosdok/id00001330 urn:nbn:de:gbv:28-diss2014-0082-2 This thesis studies minimal lattice-free symmetric polytopes. Lattice-free means that the only integral points in the polytope are its vertices. Symmetric in context of the thesis means that all vertices lie in one single orbit under a group action. The thesis focuses on groups that are permutation groups acting on R^n by permuting coordinates. If a symmetric polytope is lattice-free, its vertices are called core points. Methods to construct core points and applications in symmetric integer linear programming are explored.