S4:{4,6}

Statistics

genus c	4, orientable
Schläfli formula c	{4,6}
V / F / E c	12 / 18 / 36
notes
vertex, face multiplicity c	1, 1
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	18, each with 4 edges 12, each with 6 edges 12, each with 6 edges 18, each with 4 edges 18, each with 4 edges
antipodal sets	9 of ( 2v ), 6 of ( 2f ), 18 of ( 2e ), 9 of ( 2h ), 6 of ( 2p2 )
rotational symmetry group	72 elements.
full symmetry group	144 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, s6, srs‑1r2s‑1rs >
C&D number c	R4.3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{6,4}.

It is self-Petrie dual.

It is a 2-fold cover of N5:{4,6}.

It can be 5-split to give R52.5′.
It can be 7-split to give R76.13′.

List of regular maps in orientable genus 4.

Wireframe construction

	×	{6,3}(0,2)	C.Séquin

Underlying Graph

Its skeleton is K_6,6.

Other Regular Maps

General Index

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