The Genus-C5 Regular Map {6,6}

This regular map has three hexagonal faces, three 6-valent vertices, and nine edges. Each face borders each other face three times (i.e. its face-multiplicity is 3), and each vertex is connected by three edges to each of the other two edges (i.e. its vertex-multiplicity is 3).

Its is self-dual. It is cantankerous, see W89. It is the shuriken of S1{6,3}(o,2). It can be cantellated to give {6,4}. Its Petrie dual is S1{3,6}(0,2).

Its rotational symmetry group has order 36.

Its Petrie polygons are triangles, its holes are digons, its order-2 Petrie polygons are hexagons, and its order-3 holes are hexagons which comprise just three edges of the regular map, each in both directions.

It is the shuriken of S1{6,3}(0,2)

Other regular maps on the genus-C5 non-oriented surface.
Index to other pages on regular maps.
Some pages on groups

Copyright N.S.Wedd 2010