S4:{6,12}

Statistics

genus c4, orientable
Schläfli formula c{6,12}
V / F / E c 2 / 4 / 12
notesFaces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c12, 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 double, 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 sets1 of ( 2v ), 2 of ( 2f ), 6 of ( 2e )
rotational symmetry groupC3 ⋊ D8, with 24 elements
full symmetry group48 elements.
its presentation c< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, s‑1r3s‑1r, s‑2r2s‑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:{12,6}.

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

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

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