Gabriel Cunningham: Finite 3-orbit skeletal polyhedra

Seminarja iz diskretne matematike v torek, 5. januarja ne bo, so pa vsi udeleženci vabljeni na predavanje Gabriela Cunninghama v okviru mednarodnega seminarja iz algebraične teorije grafov.

The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join them and other colleagues on January 5, 2021, at 7pm Central European Time, for the next presentation delivered by Gabriel Cunningham.

He will speak on Finite 3-orbit skeletal polyhedra.


Abstract: A skeletal polyhedron is a graph embedded in space where certain simple cycles are designated as faces, subject to some ``geometric'' restrictions. The symmetry group of a skeletal polyhedron consists of the isometries that preserve the graph and the face structure. A skeletal polyhedron is k-orbit if the symmetry group has k orbits on the flags (consisting of a vertex, an edge at that vertex, and a face using that edge). The regular (1-orbit) skeletal polyhedra in E^3 are the 48 Gr\"{u}nbaum-Dress polyhedra. One of the classes of 2-orbit skeletal polyhedra (the chiral ones) were classified by Egon Schulte in 2004-2005. In this talk, I will give a brief history of highly-symmetric polyhedra, and then I will discuss joint work with Daniel Pellicer where we are classifying the finite 3-orbit skeletal polyhedra. Unlike regular and 2-orbit polyhedra, there are finite skeletal 3-orbit polyhedra in E^2. We will also see that although in principle, the symmetry group of a skeletal polyhedron might be a proper subgroup of the automorphism group of its graph, in a surprising number of cases that we encounter in our classification, the two groups coincide.


This talk will have no Cayley graphs, but circulant graphs do feature prominently.

Join Zoom Meeting at
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Further details may be found at http://euler.doa.fmph.uniba.sk/AGTIW.html
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