S4:{3,12}

Statistics

genus c	4, orientable
Schläfli formula c	{3,12}
V / F / E c	6 / 24 / 36
notes
vertex, face multiplicity c	3, 1
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	12, each with 6 edges 6, each with 12 edges 18, each with 4 edges 24, each with 3 edges 12, each with 6 edges 12, each with 6 edges 36, each with 2 edges 24, each with 3 edges 12, each with 6 edges 18, each with 4 edges
rotational symmetry group	72 elements.
full symmetry group	144 elements.
its presentation c	< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, (sr‑1s)3, srs‑3rs4 >
C&D number c	R4.1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{12,3}.

Its Petrie dual is N20.3.

It can be 2-split to give R19.18.
It can be 4-split to give R49.67.
It can be 5-split to give R64.27′.
It can be 7-split to give R94.10′.

It can be obtained by triambulating S4:{6,6}3,2.

It is its own 5-hole derivative.

It can be stellated (with path <1,-1>) to give S4:{6,12} . The density of the stellation is 3.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 3 . K_2,2,2.

Comments

The 4th-order holes have six edges, but involve only three distinct edges and two distinct vertices.

Other Regular Maps

General Index

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