This genus-2 regular map, shown to the right, has two hexagonal faces, each meeting three times at each of its 2 vertices. It has six edges, and a Euler characteristic of -2.

It is self-dual.
Its double cover is S^{3}:{6,6}.
It can be cantellated to produce S^{2}:{6,4}.

Its Petrie dual is the 6-hosohedron.

Its rotational symmetry group is D12.

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

Its Petrie polygons have two edges. Its holes have six edges. Its 2nd-order Petrie polygons have two edges. Its 3rd-order holes have two edges.

Each face is antipodal to the other; each vertex is antipodal to the other; the six 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-2 oriented surface.

Index to other pages on regular maps.

Some pages on groups

Copyright N.S.Wedd 2009