S5:{20,20}

Statistics

genus c	5, orientable
Schläfli formula c	{20,20}
V / F / E c	1 / 1 / 10
notes
vertex, face multiplicity c	20, 20
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 6th-order holes 6th-order Petrie polygons 7th-order holes 7th-order Petrie polygons 9th-order holes 9th-order Petrie polygons	10, each with 2 edges 4, each with 5 edges 10, each with 2 edges 1, with 20 edges 10, each with 2 edges 4, each with 5 edges 10, each with 2 edges 1, with 20 edges 10, each with 2 edges 1, with 20 edges 10, each with 2 edges
rotational symmetry group	C20, with 20 elements
full symmetry group	D40, with 40 elements
its presentation c	< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r‑2tr6tr‑1s  >
C&D number c	R5.16
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 its own 3-hole derivative.
It is its own 7-hole derivative.
It is its own 9-hole derivative.

It is a member of series s.

List of regular maps in orientable genus 5.

Wireframe constructions

	×	S2:{5,10}		unconfirmed
	×	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