S4:{4,5}

Statistics

genus c	4, orientable
Schläfli formula c	{4,5}
V / F / E c	24 / 30 / 60
notes
vertex, face multiplicity c	1, 1
Petrie polygons holes 2nd-order Petrie polygons	20, each with 6 edges 20, each with 6 edges 30, each with 4 edges
antipodal sets	12 of ( 2v ), 15 of ( 2f ), 30 of ( 2e )
rotational symmetry group	S5, with 120 elements
full symmetry group	240 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, s‑5, (rs‑2rs‑1)2 >
C&D number c	R4.2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{5,4}.

Its Petrie dual is R9.16′.

It is a 2-fold cover of N5:{4,5}.

Its 2-hole derivative is R9.16′.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 2 . K₆ × K₂.

Other Regular Maps

General Index

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