The Genus-2 Map {9,3}

This map is not regular. It has 12 vertices, four nonagonal faces, and 18 edges.

If it were regular, its rotational symmetry group would be C22⋊C9, the central extension of A4 by C3.

Its dual is {3,9}, and can be constructed by pyritifying S2{4,6}.

One of its Petrie polygons is a Hamiltonian dodecagon – if we embed the sructure in three-space it forms a trefoil knot. It is shown in the diagram above right with thicker lines. The other Petrie polygons are all squares. Its Petrie dual, in the projective plane, is shown to the left.

Regarded as a graph, it is the Möbius ladder of six rungs, as shown to the right. The four nonagonal faces of the map {9,3} are subgraphs, as shown below.


Other regular maps on the genus-2 oriented surface.
Index to other pages on regular maps.
Some pages on groups

Copyright N.S.Wedd 2010