S4:{12,6}

Statistics

genus c4, orientable
Schläfli formula c{12,6}
V / F / E c 4 / 2 / 12
notesFaces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 12
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6 Hamiltonian, each with 4 edges
4 double, each with 6 edges
12, each with 2 edges
6 Hamiltonian, each with 4 edges
antipodal sets2 of ( 2v ), 1 of ( 2f ), 6 of ( 2e )
rotational symmetry groupC3 ⋊ D8, with 24 elements
full symmetry group48 elements.
its presentation c< r, s, t | t2, (sr)2, (st)2, (rt)2, s6, r‑1s3r‑1s, r‑2s2r‑2 >
C&D number cR4.9′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{6,12}.

Its Petrie dual is S2:{4,6}.

It can be 5-split to give R20.4′.
It can be 7-split to give R28.24′.
It can be 11-split to give R44.4′.

It is a member of series q.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 3 . 4-cycle.

Other Regular Maps

General Index

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