On the Complexity of Polytope Isomorphism Problems

@article{Kaibel2003OnTC,
  title={On the Complexity of Polytope Isomorphism Problems},
  author={Volker Kaibel and Alexander Schwartz},
  journal={Graphs and Combinatorics},
  year={2003},
  volume={19},
  pages={215-230}
}
We show that the problem to decide whether two (convex) polyt opes, given by their vertex-facet incidences, are combinatorial ly somorphic is graph isomorphism complete, even for simple or simplicial polytopes . On the other hand, we give a polynomial time algorithm for the combinatorial po yt pe isomorphism problem in bounded dimensions. Furthermore, we derive that the problems to decide whether two polytopes, given either by vertex or by face t descriptions, are projectively or affinely… CONTINUE READING