C5:{6,6}

Statistics

genus c5, non-orientable
Schläfli formula c{6,6}
V / F / E c 3 / 3 / 9
notesFaces share vertices with themselves replete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 3
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6 Hamiltonian, each with 3 edges
9, each with 2 edges
3 double, each with 6 edges
3 Hamiltonian, each with 6 edges
antipodal sets3 of ( v, p2 ), 3 of ( f, h3 ), 9 of ( e, h )
rotational symmetry groupD6×D6, with 36 elements
full symmetry groupD6×D6, with 36 elements
its presentation c< r, s, t | t2, (rs)2, (rs‑1)2, (rt)2, (st)2, r6, s6, s‑1r‑3s2t  >
C&D number cN5.4
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 {3,6}(0,2).

It can be 2-fold covered to give S4:{6,6}3,3.

It can be rectified to give C5:{6,4}.

It is the half shuriken of {6,3}(0,2).

List of regular maps in non-orientable genus 5.

Underlying Graph

Its skeleton is 3 . K3.

Other Regular Maps

General Index

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