S2:{5,10}

Statistics

genus c	2, orientable
Schläfli formula c	{5,10}
V / F / E c	1 / 2 / 5
notes
vertex, face multiplicity c	10, 5
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons 5th-order holes 5th-order Petrie polygons	5, each with 2 edges 1, each with 10 edges 5, each with 2 edges 2, each with 5 edges 5, each with 2 edges 1, each with 10 edges 5, each with 2 edges 10, each with 1 edges 5, each with 2 edges
antipodal sets	1 of ( 2f )
rotational symmetry group	C10, with 10 elements
full symmetry group	D20, with 20 elements
its presentation c	< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r‑5 >
C&D number c	R2.4
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{10,5}.

Its Petrie dual is the hemi-10-hosohedron.

It can be 2-split to give S4:{10,10}.

It can be rectified to give rectification of S2:{10,5}.

It is its own 3-hole derivative.

It is a member of series α .

List of regular maps in orientable genus 2.

Underlying Graph

Its skeleton is 5 . 1-cycle.

Other Regular Maps

General Index

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