S4:{4,10}

Statistics

genus c	4, orientable
Schläfli formula c	{4,10}
V / F / E c	4 / 10 / 20
notes
vertex, face multiplicity c	5, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons	2, each with 20 edges 20, each with 2 edges 4, each with 10 edges 10, each with 4 edges 2, each with 20 edges 20, each with 2 edges 4, each with 10 edges
rotational symmetry group	40 elements.
full symmetry group	80 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s10 >
C&D number c	R4.4
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{10,4}.

Its Petrie dual is R8.8′.

It can be 3-split to give R20.7′.
It can be 5-split to give R36.16′.
It can be 7-split to give R52.9′.
It can be 9-split to give R68.6′.
It can be 11-split to give R84.6′.

It is its own 3-hole derivative.

It is a member of series ζ.

List of regular maps in orientable genus 4.

Wireframe constructions

	×	the 5-hosohedron
	×	the 5-hosohedron
	×	S2:{10,5}

Underlying Graph

Its skeleton is 5 . 4-cycle.

Other Regular Maps

General Index

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