The Heawood map


genus c1, orientable
Schläfli formula c{6,3}
V / F / E c 14 / 7 / 21
notesChiral replete singular is a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 1
Petrie polygons
3, each with 14 edges
antipodal sets7 of ( 2v, f ), 7 of ( 3e )
rotational symmetry groupC7⋊C6, with 42 elements
full symmetry groupC7⋊C6, with 42 elements
C&D number cC1.t1-3′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the dual Heawood map.

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

It can be 3-fold covered to give {6,3}(3,5).

It can be rectified to give rectification of {6,3}(1,3).

List of regular maps in orientable genus 1.

Underlying Graph

Its skeleton is Heawood graph.


Each of the seven hexagons borders each of the other six.

It can be embedded in three-space, with flat non-intersecting (but irregular) faces, as the Szilassi polyhedron.

Other Regular Maps

General Index

The image on this page is copyright © 2010 N. Wedd