S4:{6,6}3,3

Statistics

genus c4, orientable
Schläfli formula c{6,6}
V / F / E c 6 / 6 / 18
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 3
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6, each with 6 edges
18, each with 2 edges
6, each with 6 edges
6 Hamiltonian, each with 6 edges
antipodal sets3 of ( 2v, 2p2 ), 3 of ( 2f, 2h3 ), 9 of ( 2e, 2h ), 3 of ( 2p )
rotational symmetry group36 elements.
full symmetry group72 elements.
its presentation c< r, s, t | t2, (rs)2, (rs‑1)2, (rt)2, (st)2, r6, s6 >
C&D number cR4.7
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

Its Petrie dual is S4:{6,6}3,2.

It is a 2-fold cover of C5:{6,6}.

It can be 5-split to give R28.23′.
It can be 7-split to give R40.6′.
It can be 11-split to give R64.21′.

It can be rectified to give S4:{6,4}.
It can be rectified to give S4:{6,6}3,3.

List of regular maps in orientable genus 4.

Wireframe construction

w  {6,6}  2/3 | 2/3 | 2 × {6,3}(0,2)

Underlying Graph

Its skeleton is 3 . 6-cycle.

Other Regular Maps

General Index

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