This regular map is in genus-C6 (a sphere plus six crosscaps). It has twenty triangular faces, 20 vertices and 30 edges, giving a Euler characteristic of -4.
Its dual is C6:{10,3}5.
Its rotational symmetry group is S5.
Its Petrie polygons have five edges. It is the Petrie dual of the dodecahedron S0:{5,3}.
It is different from C6:{10,3}10. C6:{10,3}5 has a girth (minimal loop) of five edges, C6:{10,3}10 has a girth of six.
The faces form antipodal pairs (shown in the same colour in the diagram). The edges form antipodal pairs. Each vertex is antipodal to a Petrie polygon.
Other regular maps on the genus-C6 surface.
Index to other pages on regular maps.
Copyright N.S.Wedd 2009