S4:{6,6}3,2

Statistics

genus ^c	4, orientable
Schläfli formula ^c	{6,6}
V / F / E ^c	6 / 6 / 18
notes
vertex, face multiplicity ^c	3, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	6, each with 6 edges 6, each with 6 edges 18, each with 2 edges 6, each with 6 edges 6, each with 6 edges
antipodal sets	3 of ( 2v ), 3 of ( 2e )
rotational symmetry group	36 elements.
full symmetry group	72 elements.
its presentation ^c	< r, s, t \| t², (sr)², (st)², (rt)², s⁶, r^‑1s³r^‑1s, r⁶ >
C&D number ^c	R4.8′
The statistics marked ^c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{6,6}2,3.

Its Petrie dual is S4:{6,6}3,3.

It can be 5-split to give R28.22′.
It can be 7-split to give R40.7′.
It can be 11-split to give R64.20′.
It can be built by 2-splitting {3,6}_(0,2).

It can be triambulated to give S4:{3,12}.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 3 . 6-cycle.

Comments

This regular map appears, in a very different presentation, on page 46 of ^H01, where it is considered as a dessin d'enfant. The graph is bipartite, and the actions of the dessin act on the edges of the graph to generate S3×C3. The authors obtained it by a method they term "origami".

Other Regular Maps

General Index