S3:{12,4}

Statistics

genus c	3, orientable
Schläfli formula c	{12,4}
V / F / E c	6 / 2 / 12
notes
vertex, face multiplicity c	2, 12
Petrie polygons holes 2nd-order Petrie polygons	4, each with 6 edges 12, each with 2 edges 12, each with 2 edges
antipodal sets	3 of ( 2v ), 1 of ( 2f ), 6 of ( 2e ), 2 of ( 2p2 )
rotational symmetry group	D6×C4, with 24 elements
full symmetry group	48 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r‑3s2r‑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:{4,12}.

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

It can be 5-split to give R15.8′.
It can be 7-split to give R21.13′.
It can be 11-split to give R33.30′.

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

It is a member of series j.

List of regular maps in orientable genus 3.

Wireframe construction

	×	{3,6}(1,1)	w09.22

Underlying Graph

Its skeleton is 2 . 6-cycle.

Other Regular Maps

General Index

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