S2:{8,4}

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Statistics

genus c	2, orientable
Schläfli formula c	{8,4}
V / F / E c	4 / 2 / 8
notes
vertex, face multiplicity c	2, 8
Petrie polygons holes	2 Eulerian, each with 8 edges 8, each with 2 edges
antipodal sets	2 of ( 2v ), 1 of ( 2f ), 4 of ( 2e )
rotational symmetry group	quasidihedral(16), with 16 elements
full symmetry group	32 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (sr-1)2, (st)2, (rt)2, r-2s2r-2 >.
C&D number c	R2.3′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{4,8}.

It is self-Petrie dual.

It can be 2-fold covered to give S3:{8,4|4}.
It can be 2-fold covered to give S3:{8,4|2}.

It can be rectified to give rectification of S2:{8,4}.
It is the result of rectifying S2:{8,8}.

It is a member of series j.

Other regular maps in the same manifold.

Underlying Graph

If we ignore its faces and regard it as a graph, it is isomorphic to a double 4-cycle.

Comments

This regular map features in the movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps.

Other Regular Maps

General Index

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