

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 
7, each with 6 edges  
rotational symmetry group  C7⋊C3, with 21 elements 
full symmetry group  C7⋊C6, with 42 elements 
Its Petrie dual is
It can be pyritified (type 14/3/7/3) to give
List of regular maps in orientable genus 3.
Its skeleton is Heawood graph.
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.
Orientable  
Nonorientable 
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