S5:{20,20}

Statistics

genus c5, orientable
Schläfli formula c{20,20}
V / F / E c 1 / 1 / 10
notesFaces share vertices with themselves Faces share edges with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c20, 20
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
10, each with 2 edges
4, each with 5 edges
10, each with 2 edges
1 double Eulerian, with 20 edges
10, each with 2 edges
rotational symmetry groupC20, with 20 elements
full symmetry groupD40, with 40 elements
its presentation c< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r‑2tr6tr‑1s  >
C&D number cR5.16
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

It can be rectified to give S5:{20,4}.

It is a member of series s.

List of regular maps in orientable genus 5.

Wireframe constructions

x  {20,20}  2/10 | 2/10 | 2 × S2:{5,10} unconfirmed
y  {20,20}  2/10 | 2/10 | 2 × S2:{5,10}

Underlying Graph

Its skeleton is 10 . 1-cycle.

Other Regular Maps

General Index

The image on this page is copyright © 2010 N. Wedd