The dual Heawood map


genus c1, orientable
Schläfli formula c{3,6}
V / F / E c 7 / 14 / 21
notesChiral replete singular is a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 1
Petrie polygons
2nd-order Petrie polygons
3rd-order holes
3 double Hamiltonian, each with 14 edges
7, each with 6 edges
3 double Hamiltonian, each with 14 edges
6 Hamiltonian, each with 7 edges
antipodal sets7 of ( v, h2, 2f ), 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 Heawood map.

It can be 3-fold covered to give {3,6}(3,5).
It can be 7-fold covered to give {3,6}(2,8).
It is a 7-fold cover of {3,6}(1,1).

It can be 2-split to give C8.1′.

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

It can be truncated to give {6,3}(3,5).

List of regular maps in orientable genus 1.

Underlying Graph

Its skeleton is K7.


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

Other Regular Maps

General Index

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