S5:{20,4}

Statistics

genus c	5, orientable
Schläfli formula c	{20,4}
V / F / E c	10 / 2 / 20
notes
vertex, face multiplicity c	2, 20
Petrie polygons holes 2nd-order Petrie polygons	4, each with 10 edges 20, each with 2 edges 20, each with 2 edges
rotational symmetry group	40 elements.
full symmetry group	80 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r5sr‑4sr  >
C&D number c	R5.8′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S5:{4,20}.

Its Petrie dual is S4:{10,4}.

It can be 3-split to give R15.8′.
It can be 7-split to give R35.3′.
It can be 9-split to give R45.11′.
It can be 11-split to give R55.15′.

It is the result of rectifying S5:{20,20}.

It is a member of series ζ'°.

List of regular maps in orientable genus 5.

Wireframe construction

	×	S2:{5,10}

Underlying Graph

Its skeleton is 2 . 10-cycle.

Other Regular Maps

General Index

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