S2:{6,6}

Statistics

genus c2, orientable
Schläfli formula c{6,6}
V / F / E c 2 / 2 / 6
notestrivial Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c6, 6
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6, each with 2 edges
2 double, each with 6 edges
6, each with 2 edges
6, each with 2 edges
antipodal sets1 of ( 2v ), 1 of ( 2f ), 3 of ( 2e )
rotational symmetry groupC6×C2, with 12 elements
full symmetry groupD6×C2×C2, with 24 elements
its presentation c< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r6 >
C&D number cR2.5
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

Its Petrie dual is the 6-hosohedron.

It can be built by 2-splitting {3,6}(1,1).

It can be rectified to give S2:{6,4}.

It can be derived by stellation (with path <1,-1;-1,1>) from {6,3}(1,1). The density of the stellation is 4.

It is a member of series k.
It is a member of series p.
It is a member of series q.

List of regular maps in orientable genus 2.

Underlying Graph

Its skeleton is 6 . K2.

Other Regular Maps

General Index

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