C5:{5,5}

Statistics

genus c5, non-orientable
Schläfli formula c{5,5}
V / F / E c 6 / 6 / 15
notesreplete singular is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
10, each with 3 edges
10, each with 3 edges
6, each with 5 edges
antipodal sets6 of ( v, f, p2 ), 10 of ( p, h )
rotational symmetry groupA5, with 60 elements
full symmetry groupA5, with 60 elements
its presentation c< r, s, t | t2, (rs)2, (rt)2, (st)2, r‑5, (s‑1r)3, rs‑1r‑2s‑2t >
C&D number cN5.3
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 the hemi-icosahedron.

It can be 2-fold covered to give S4:{5,5}.

It can be 2-split to give N14.2′.

It can be rectified to give C5:{5,4}.

It is the diagonalisation of C5:{8,4}.

List of regular maps in non-orientable genus 5.

Underlying Graph

Its skeleton is K6.

Other Regular Maps

General Index

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