This genus-3 regular map, shown to the right, has one dodecagonal face, meeting itself twelve times at the single vertex. It has six edges, and a Euler characteristic of -4.

It is self-dual.
Its Petrie dual is the 6-hemihosohedron.
It can be cantellated to produce S^{3}:{12,4}.

Its rotational symmetry group is D12.

The face shares all its vertices and all its edges with itself. The edges join a vertex to itself. Some readers may consider that this invalidates it as a regular map.

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

The face is antipodal to the vertex, and vice versa. The six edges form a single antipodal set. Rotating any one edge about its centre causes every other edge to remain where it is and rotate about its own centre: this is the involution of its rotational symmetry group.

It is possible to insert another face so as to convert this map
to the regular map C^{6}:{4,20}.

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