The Genus-C6 Regular Map {3,10}5

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.

Antipodal Faces and Vertices

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