N7:{4,9}

Statistics

genus c	7, non-orientable
Schläfli formula c	{4,9}
V / F / E c	4 / 9 / 18
notes
vertex, face multiplicity c	3, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons	4 Hamiltonian, each with 9 edges 18, each with 2 edges 4, each with 9 edges 9 Hamiltonian, each with 4 edges 12, each with 3 edges 18, each with 2 edges 4, each with 9 edges
antipodal sets	4 of ( v, p, 2p ), 9 of ( f, 3h )
rotational symmetry group	72 elements.
full symmetry group	72 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, rs‑1r2st, s‑9  >
C&D number c	N7.2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is N7:{9,4}.

Its Petrie dual is S6:{9,9}.

It can be 2-fold covered to give S6:{4,9}.

It is a member of series ν .

List of regular maps in non-orientable genus 7.

Underlying Graph

Its skeleton is 3 . K₄.

Comments

Each face is complementary to (as well as antipodal to) a Petrie polygon. For a face-Petrie polygon pair, each edge is a member of one or the other.

Other Regular Maps

General Index

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