S3:{6,6}

Statistics

genus c	3, orientable
Schläfli formula c	{6,6}
V / F / E c	4 / 4 / 12
notes
vertex, face multiplicity c	2, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	6, each with 4 edges 8, each with 3 edges 6, each with 4 edges 12, each with 2 edges 12, each with 2 edges
antipodal sets	4 of ( v, h ), 6 of ( 2e )
rotational symmetry group	A4×C2, with 24 elements
full symmetry group	48 elements.
its presentation c	< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, s‑1r3s‑2 >
C&D number c	R3.8
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 N4:{4,6}₆.

It can be rectified to give S3:{6,4}.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is 2 . K₄.

Other Regular Maps

General Index

The images on this page are copyright © 2010 N. Wedd