Highly Influenced

@article{Effenberger2010HamiltonianSO, title={Hamiltonian Submanifolds of Regular Polytopes}, author={Felix Effenberger and Wolfgang K{\"u}hnel}, journal={Discrete & Computational Geometry}, year={2010}, volume={43}, pages={242-262} }

- Published 2010 in Discrete & Computational Geometry
DOI:10.1007/s00454-009-9151-9

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