S2:{5,10}

Statistics

genus c2, orientable
Schläfli formula c{5,10}
V / F / E c 1 / 2 / 5
notestrivial Faces share vertices with themselves Vertices share edges with themselves is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c10, 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
5, each with 2 edges
1 Eulerian, with 10 edges
5, each with 2 edges
2, each with 5 edges
5, each with 2 edges
1 Eulerian, with 10 edges
5, each with 2 edges
10, each with 1 edges
antipodal sets1 of ( 2f )
rotational symmetry groupC10, with 10 elements
full symmetry groupD20, with 20 elements
its presentation c< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r‑5 >
C&D number cR2.4
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 a member of series z.

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