The Genus-3 Regular Map {14,7}

This genus-3 regular map, shown to the right, has one 14-gonal face, meeting itself six times at each of its vertices. It has seven edges, and a Euler characteristic of -2.

Its dual is S3:{7,14}. Its Petrie dual is the 7-hosohedron.

Its rotational symmetry group is D14.

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

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

Antipodal Faces and Vertices

Each vertex is antipodal to the other; the seven edges form a single antipodal set. Rotating one edge about its centre causes every other edge to remain where it is and rotate about its centre: this is the central involution of its rotational symmetry group.


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