S3:{4,12}

Statistics

genus c3, orientable
Schläfli formula c{4,12}
V / F / E c 2 / 6 / 12
notesFaces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c12, 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 6 edges
12, each with 2 edges
4, each with 6 edges
6, each with 4 edges
12, each with 2 edges
12, each with 2 edges
4, each with 6 edges
antipodal sets1 of ( 2v ), 3 of ( 2f ), 6 of ( 2e )
rotational symmetry groupD6×C4, with 24 elements
full symmetry group48 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s‑3r2s‑3 >
C&D number cR3.7
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S3:{12,4}.

Its Petrie dual is S4:{6,12}.

It can be rectified to give rectification of S3:{12,4}.

It is a member of series h.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is 12 . K2.

Other Regular Maps

General Index

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