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

This regular map is in genus-C6 (a sphere plus six crosscaps). It has six decagonal faces, each meeting each of the others twice. It has 20 vertices and 30 edges, giving a Euler characteristic of -4.

Its dual is C6:{3,10}.

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 vertices form antipodal pairs. The edges form antipodal pairs. Each face 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