S3:{4,8|4}

Statistics

genus c	3, orientable
Schläfli formula c	{4,8}
V / F / E c	4 / 8 / 16
notes
vertex, face multiplicity c	4, 1
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes	4, each with 8 edges 8, each with 4 edges 16, each with 2 edges 8, each with 4 edges 4, each with 8 edges 16, each with 2 edges
antipodal sets	2 of ( 2v ), 4 of ( 2f )
rotational symmetry group	32 elements.
full symmetry group	64 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, srs‑1rs2 >
C&D number c	R3.5
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S3:{8,4|4}.

Its Petrie dual is R5.12.

It is a 2-fold cover of S2:{4,8}.

It can be 3-split to give R15.14′.
It can be 5-split to give R27.7′.
It can be 7-split to give R39.7′.
It can be 9-split to give R51.21′.
It can be 11-split to give R63.9′.

It can be rectified to give rectification of S3:{8,4|4}.

It can be truncated to give the Dyck map.

It is its own 3-hole derivative.

It can be derived by stellation (with path <1,-1>) from the dual Dyck map. The density of the stellation is 3.

It is a member of series ι.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is 4 . 4-cycle.

Other Regular Maps

General Index

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