This genus-2 regular map, shown to the right, has six octagonal faces, of which three meet at each of its 16 vertices. It has 24 edges, and a Euler characteristic of -2.

Its Petrie polygons have 12 edges.
Its Petrie dual is S^{3}{12,3}.

Its dual is {3,8}.
Its double cover is S^{3}:{8,3}.

The diagram to the right may make its symmetry clearer. Note that the dark and the pale blue faces do not touch, nor the dark and pale red, nor the dark and pale green. Otherwise, each face borders each other face twice.

In this diagram the edges themselves have been coloured: each red edge separates
a blue face from a green face, and has a dark red face at one end and a pale red
face at the other end; and likewise for blue, and green, edges.

Each face is antipodal to one other face: dark red to pale red, etc. Each vertex is antipodal to one other vertex, as indicated by the black spots in the diagram to the right. Each edge is antipodal to one other edge.

The diagram to the left shows the same map {8,3} in a less pleasing way.

This regular map can be used to draw Cayley graphs for the
Pauli group and
for GL(2,3): see
Some Cayley Diagrams drawn on the
surface of Genus 2.

Other regular maps on the genus-2 oriented surface.

Index to other pages on regular maps.

Some pages on groups

Copyright N.S.Wedd 2009