Some Cayley Diagrams drawn on the surface of Genus 2

Tucker's Genus 2 Group
Tucker's Genus 2 Group

There is only one group such that a Cayley diagram with no crossings can be drawn for it in the surface of genus 2 but on no surface of lower genus. This is Tucker's Group, with 96 elements. Its Cayley diagram is shown to the right.

The Pauli group

To the left are some more Cayley diagrams drawn on the oriented surface of genus 2. They could have been drawn without crossings on an oriented surface of lower genus, but I found the diagrams below pleasingly symmetrcal.

The pink arrows around the edge of each diagram are "sewing instructions", showing how it is to be assembled into a genus 2 surface, or torus.

You can hover over any diagram to find what group it portrays.

Regular maps drawn on the surface of genus 2.
Some more Cayley diagrams drawn on surfaces appropriate to their genus.
Some more Cayley diagrams and other pages on groups
Copyright N.S.Wedd 2009