S3:{6,6}

Statistics

genus c3, orientable
Schläfli formula c{6,6}
V / F / E c 4 / 4 / 12
notesFaces share vertices with themselves replete is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c2, 2
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6, each with 4 edges
8, each with 3 edges
6, each with 4 edges
12, each with 2 edges
antipodal sets4 of ( v, h ), 6 of ( 2e )
rotational symmetry groupA4×C2, with 24 elements
full symmetry group48 elements.
its presentation c< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, s‑1r3s‑2 >
C&D number cR3.8
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 C4:{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