C6:{4,5}

Statistics

genus c6, non-orientable
Schläfli formula c{4,5}
V / F / E c 16 / 20 / 40
notesreplete singular is a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
16, each with 5 edges
20, each with 4 edges
16, each with 5 edges
antipodal sets10 of ( 2f ), 16 of ( 2e )
rotational symmetry group160 elements.
full symmetry group160 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, s‑5, (rs‑1)4, s‑1trs‑1r‑2s‑1rsr‑1s‑1  >
C&D number cN6.3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is C6:{5,4}.

Its Petrie dual is S5:{5,5}.

It can be 2-fold covered to give S5:{4,5}.

It can be rectified to give rectification of C6:{5,4}.

It is its own 2-hole derivative.

List of regular maps in non-orientable genus 6.

Underlying Graph

Its skeleton is Clebsch graph.

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