genus c4, non-orientable
Schläfli formula c{6,4}
V / F / E c 6 / 4 / 12
notesreplete cantankerous is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 2
Petrie polygons
4 Hamiltonian, each with 6 edges
6 double, each with 4 edges
antipodal sets3 of ( 2v ), 4 of ( f, p ), 6 of ( 2e ), 3 of ( 2h )
rotational symmetry group48 elements.
full symmetry group48 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, sr‑1s2rt, r6 >
C&D number cN4.1′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is C4:{4,6}6.

It is self-Petrie dual.

It can be 2-fold covered to give S3:{6,4}.

It can be 5-split to give N28.2′.
It can be 7-split to give N40.1′.
It can be 11-split to give N64.1′.
It can be built by 2-splitting the hemioctahedron.

It can be rectified to give rectification of C4:{6,4}6.

List of regular maps in non-orientable genus 4.

Underlying Graph

Its skeleton is 2 . 6-cycle.

Other Regular Maps

General Index

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