S4:{4,10}

Statistics

genus c4, orientable
Schläfli formula c{4,10}
V / F / E c 4 / 10 / 20
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c5, 2
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-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
rotational symmetry group40 elements.
full symmetry group80 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s10 >
C&D number cR4.4
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{10,4}.

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 a member of series m.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 5 . 4-cycle.

Other Regular Maps

General Index

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