Department of Mathematics

Symmetries of discrete objects

This research deals with discrete objects such as graphs, networks, maps, tessellated surfaces, polytopes and 3-manifolds, which have high degrees of symmetry under particular conditions.

The Petersen Graph

Typically, the symmetries form a group that can be presented in a particular form, this is associated with the kind of object being considered. Examples can be analysed in terms of the object itself, or the group, or even the ambient space.

Also new examples, or new families of examples, can be constructed using knowledge of the group structure. Use of the computational algebra package MAGMA can be very helpful in their construction and analysis and in solving open problems.

A regular map of type {4,6} and genus 11

Researchers at The University of Auckland


Plus research colleagues in Germany, Korea, Mexico, Slovakia, Slovenia, Spain, Sweden, the United Kingdom and the United States of America.

Research is supported by the New Zealand Marsden Fund.