


genus ^{c}  4, orientable 
Schläfli formula ^{c}  {6,6} 
V / F / E ^{c}  6 / 6 / 18 
notes  
vertex, face multiplicity ^{c}  3, 2 
6 Hamiltonian, each with 6 edges 6 double, each with 6 edges 18, each with 2 edges 6 Hamiltonian, each with 6 edges  
antipodal sets  3 of ( 2v ), 3 of ( 2e ) 
rotational symmetry group  36 elements. 
full symmetry group  72 elements. 
its presentation ^{c}  < r, s, t  t^{2}, (sr)^{2}, (st)^{2}, (rt)^{2}, s^{6}, r^{‑1}s^{3}r^{‑1}s, r^{6} > 
C&D number ^{c}  R4.8′ 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It can be 5split to give
It can be 7split to give
It can be 11split to give
It can be built by 2splitting
It can be triambulated to give
List of regular maps in orientable genus 4.
Its skeleton is 3 . 6cycle.
This regular map appears, in a very different presentation, on page 46 of ^{H01}, where it is considered as a dessin d'enfant. The graph is bipartite, and the actions of the dessin act on the edges of the graph to generate S3×C3. The authors obtained it by a method they term "origami".
Orientable  
Nonorientable 
The images on this page are copyright © 2010 N. Wedd