Hamiltonian Submanifolds of Regular Polytopes

  title={Hamiltonian Submanifolds of Regular Polytopes},
  author={Felix Effenberger and Wolfgang K{\"u}hnel},
  journal={Discrete & Computational Geometry},
We investigate polyhedral 2k-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex k-Hamiltonian if it contains the full k-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called super-neighborly triangulations) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided… CONTINUE READING