19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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Methods and Open Problems in the Theory of Regular Covers of Polyhedra

Presented by Dr. Gordon WILLIAMS
Type: Oral presentation
Track: Polytopes and Incidence Geometries


{\em Abstract polytopes} are partially ordered sets that mimic many of the combinatorial properties of the face lattice of a polytope. {\em Regular} abstract polytopes are the most symmetric class of these objects, and their study and interest has been greatly assisted by their almost magical correspondence to a special class of groups generated by involutions known as {\em string C-groups}. Less well understood are the abstract polytopes that lack this high degree of symmetry. This talk will review several methods for the construction of representations of polyhedra as quotients of regular abstract polytopes. Special attention will be paid to recent work on the representations of non-finite polyhedra as quotients of regular tilings of the hyperbolic plane, with the Archimedean tilings as our motivating examples. This talk will also include a discussion of some of the current lines of inquiry motivated by the study of these representations, as well as open problems in the area. This talk incorporates joint work with Michael Hartley, Barry Monson and Daniel Pellicer.


Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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