S4:{9,18}

Statistics

genus c4, orientable
Schläfli formula c{9,18}
V / F / E c 1 / 2 / 9
notesFaces share vertices with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c18, 9
Petrie polygons
9, each with 2 edges
rotational symmetry groupC18, with 18 elements
full symmetry groupD18×C2, with 36 elements
its presentation c< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, rs‑1tsr‑5tr >
C&D number cR4.10
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{18,9}.

It can be 2-split to give R8.10.

It is a member of series z.

List of regular maps in orientable genus 4.


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