S3:{14,3}a

Statistics

genus ^c	3, orientable
Schläfli formula ^c	{14,3}
V / F / E ^c	14 / 3 / 21
notes	This is not a regular map.
vertex, face multiplicity ^c	1, 7
Petrie polygons	7, each with 6 edges
rotational symmetry group	C7⋊C3, with 21 elements
full symmetry group	C7⋊C6, with 42 elements

Relations to other Regular Maps

Its dual is S3:{3,14}a.

Its Petrie dual is the Heawood map.

It can be pyritified (type 14/3/7/3) to give the Klein map.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is Heawood graph.

Comments

This irregular map can be constructed from S3:{7,3} by choosing a set of three mutually antipodal faces, painting them three different colours, painting each of the remaining 21 faces to match its coloured neighbour, and finally removing all edges that separate two faces of the same colour.

Its symmetry group has size 21, smaller than you might think. This is because if we rotate one face, the other faces undergo permutations of their vertices which are not rotations.

Other Regular Maps

General Index