{3,6}(2,2)

Statistics

genus c1, orientable
Schläfli formula c{3,6}
V / F / E c 4 / 8 / 12
notesreplete is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c2, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
6, each with 4 edges
4, each with 6 edges
6, each with 4 edges
12, each with 2 edges
12, each with 2 edges
antipodal sets4 of ( v, h2 )
rotational symmetry groupA4×C2, with 24 elements
full symmetry groupS4×C2, with 48 elements
C&D number cR1.t2-2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is {6,3}(2,2).

Its Petrie dual is N4:{4,6}3.

It can be 3-fold covered to give {3,6}(0,4).
It can be 7-fold covered to give {3,6}(2,6).

It can be 2-split to give S5:{6,6}.

It can be rectified to give octahemioctahedron.

It can be truncated to give {6,3}(0,4).

List of regular maps in orientable genus 1.

Underlying Graph

Its skeleton is 2 . K4.

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |

The image on this page is copyright © 2010 N. Wedd