S3:{4,12}

Statistics

genus c	3, orientable
Schläfli formula c	{4,12}
V / F / E c	2 / 6 / 12
notes
vertex, face multiplicity c	12, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons	4, each with 6 edges 12, each with 2 edges 4, each with 6 edges 6, each with 4 edges 12, each with 2 edges 12, each with 2 edges 4, each with 6 edges
antipodal sets	1 of ( 2v ), 3 of ( 2f ), 6 of ( 2e )
rotational symmetry group	D6×C4, with 24 elements
full symmetry group	48 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s‑3r2s‑3 >
C&D number c	R3.7
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S3:{12,4}.

Its Petrie dual is S4:{6,12}.

It can be rectified to give rectification of S3:{12,4}.

It is a member of series h.

List of regular maps in orientable genus 3.

Wireframe construction

	×	{3,6}(1,1)

Underlying Graph

Its skeleton is 12 . K₂.

Other Regular Maps

General Index

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