S4:{6,12}

Statistics

genus c	4, orientable
Schläfli formula c	{6,12}
V / F / E c	2 / 4 / 12
notes
vertex, face multiplicity c	12, 3
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons 5th-order holes 5th-order Petrie polygons 6th-order holes	6, each with 4 edges 4, each with 6 edges 12, each with 2 edges 8, each with 3 edges 6, each with 4 edges 4, each with 6 edges 12, each with 2 edges 4, each with 6 edges 6, each with 4 edges 12, each with 2 edges
antipodal sets	1 of ( 2v ), 2 of ( 2f ), 6 of ( 2e )
rotational symmetry group	C3 ⋊ D8, with 24 elements
full symmetry group	48 elements.
its presentation c	< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, s‑1r3s‑1r, s‑2r2s‑2 >
C&D number c	R4.9
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{12,6}.

Its Petrie dual is S3:{4,12}.

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

It is its own 5-hole derivative.

It can be derived by stellation (with path <1,-1>) from S4:{3,12}. The density of the stellation is 3.

It is a member of series p.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 12 . K₂.

Other Regular Maps

General Index

The images on this page are copyright © 2010 N. Wedd