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2010

Hamiltonian Submanifolds of Regular Polytopes

13 years 11 months ago
Hamiltonian Submanifolds of Regular Polytopes
: 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 for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the d-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of S2
Felix Effenberger, Wolfgang Kühnel
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where DCG
Authors Felix Effenberger, Wolfgang Kühnel
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