Rotational Drawings of Polycyclic Configurations
by
Tomaz Pisanski
University of Ljubljana and University of Auckland (visiting)
Coauthors: Marko Boben

A configuration is said to be polycyclic if it admits an automorphism \alpha whose action on points and lines is semi-regular. The structure of a polycyclic configuration can be used in some cases to generate its special straight-line drawing in the Euclidean plane. Such a drawing is called rotational if the images of configuration points and lines in the plane are distinct (no two points or lines coincide) and the corresponding automorphism \alpha is realized as a planar rotation. This phenomenon has been studied by Branko Grünbaum and several other geometers under the name of stellar configuration. Here we present a unified approach based on voltage graphs over the cyclic group that explains why some configurations admit rotational drawings. Most results were obtained in collaboration with other mathematicians in particular with Marko Boben.

Supported in part by ``Ministrstvo za znanost in tehnologijo Slovenije'', proj. no. J1-8901-0101-99 and J2-8549-0101-99.

Date received: November 19, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafp-27.