{3,6}(1,1)

Statistics

genus c1, orientable
Schläfli formula c{3,6}
V / F / E c 1 / 2 / 3
notesFaces share vertices with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c6, 3
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3, each with 2 edges
1 double, with 6 edges
3, each with 2 edges
6, each with 1 edges
antipodal sets1 of ( 2f ), 3 of ( 2, p1, p2; 2h3 )
rotational symmetry groupC6, with 6 elements
full symmetry groupD12, with 12 elements
C&D number cR1.t1-1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is {6,3}(1,1).

Its Petrie dual is the hemi-6-hosohedron.

It can be 3-fold covered to give {3,6}(0,2).
It can be 7-fold covered to give the dual Heawood map.

It can be 2-split to give S2:{6,6}.

It can be rectified to give rectification of {6,3}(1,1).

It can be truncated to give {6,3}(0,2).

It can be stellated (with path <2,3;3,2>) to give S3{12,12} . The density of the stellation is 6.

It is a member of series q.
It is a member of series z.

List of regular maps in orientable genus 1.

Underlying Graph

Its skeleton is 3 . 1-cycle.

Other Regular Maps

General Index

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