S4:{12,6}

Statistics

genus c	4, orientable
Schläfli formula c	{12,6}
V / F / E c	4 / 2 / 12
notes
vertex, face multiplicity c	3, 12
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	6, each with 4 edges 4, each with 6 edges 12, each with 2 edges 6, each with 4 edges 6, each with 4 edges
antipodal sets	2 of ( 2v ), 1 of ( 2f ), 6 of ( 2e )
rotational symmetry group	C3 ⋊ D8, with 24 elements
full symmetry group	48 elements.
its presentation c	< r, s, t | t2, (sr)2, (st)2, (rt)2, s6, r‑1s3r‑1s, r‑2s2r‑2 >
C&D number c	R4.9′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{6,12}.

Its Petrie dual is S2:{4,6}.

It can be 5-split to give R20.4′.
It can be 7-split to give R28.24′.
It can be 11-split to give R44.4′.

It is a member of series ε'.
It is a member of series ζ°.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 3 . 4-cycle.

Other Regular Maps

General Index

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