S4:{6,6}3,3

Statistics

genus c	4, orientable
Schläfli formula c	{6,6}
V / F / E c	6 / 6 / 18
notes
vertex, face multiplicity c	3, 3
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	6, each with 6 edges 18, each with 2 edges 6, each with 6 edges 6, each with 6 edges 6, each with 6 edges
antipodal sets	3 of ( 2v, 2p2 ), 3 of ( 2f, 2h3 ), 9 of ( 2e, 2h ), 3 of ( 2p )
rotational symmetry group	36 elements.
full symmetry group	72 elements.
its presentation c	< r, s, t | t2, (rs)2, (rs‑1)2, (rt)2, (st)2, r6, s6 >
C&D number c	R4.7
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 N5:{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}.

List of regular maps in orientable genus 4.

Wireframe construction

	×	{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