N5:{6,4}

Statistics

genus c5, non-orientable
Schläfli formula c{6,4}
V / F / E c 9 / 6 / 18
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 2
Petrie polygons
holes
2nd-order Petrie polygons
9, each with 4 edges
6, each with 6 edges
12, each with 3 edges
antipodal sets9 of ( v, 2e, p ), 2 of ( 3f ), 2 of ( 3h )
rotational symmetry group72 elements.
full symmetry group72 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, r6, r‑1sr‑1s2rs‑1t, rsr‑1s2r‑1sr >
C&D number cN5.2′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is N5:{4,6}.

Its Petrie dual is {4,4}(3,0).

It can be 2-fold covered to give S4:{6,4}.

It can be rectified to give rectification of C5:{6,4}.
It is the result of rectifying N5:{6,6}.

List of regular maps in non-orientable genus 5.

Underlying Graph

Its skeleton is K3 × K3.

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