S6:{6,8}₁₂

Statistics

genus c	6, orientable
Schläfli formula c	{6,8}
V / F / E c	6 / 8 / 24
notes
vertex, face multiplicity c	2, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons	4, each with 12 edges 6, each with 8 edges 6, each with 8 edges 16, each with 3 edges 4, each with 12 edges 24, each with 2 edges INF, each with 0 edges
rotational symmetry group	48 elements.
full symmetry group	96 elements.
its presentation c	< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, (rs‑1r)2, s‑1r‑3s‑3  >
C&D number c	R6.8
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S6:{8,6}₁₂.

Its Petrie dual is N16.8′.

It can be 5-split to give R42.5′.
It can be 7-split to give R60.5′.
It can be 11-split to give R96.8′.

Its 3-hole derivative is S2:{3,8}.

List of regular maps in orientable genus 6.

Other Regular Maps

General Index

Groups of order 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 27 28 30 48 60 120 168 336 360 720