The Genus-3 Regular Map {12,4}

This genus-3 regular map, shown to the right, has two dodecagonal faces, six vertices, and 12 edges. Its Euler characteristic is -4.

Its Petrie polygons have six edges. Its holes have two edges.

Its dual is S3:{4,12}. Its Petrie dual is S2:{6,4}. It is the result of cantellating S3:{12,12}.

Its rotational symmetry group is D24.

Faces share vertices with themselvesEach face shares all its vertices with itself. Some readers may consider that this invalidates it as a regular map.


The faces form antipodal pairs, the vertices form antipodal pairs, the Petrie polygons form antipodal pairs, there are antipodal sets of four edges and two holes.

Other regular maps on the genus-3 oriented surface.
Index to other pages on regular maps.
Some pages on groups

Copyright N.S.Wedd 2009