S3:{8,4|4}

Statistics

genus c	3, orientable
Schläfli formula c	{8,4}
V / F / E c	8 / 4 / 16
notes
vertex, face multiplicity c	1, 4
Petrie polygons holes	4, each with 8 edges 8, each with 4 edges
antipodal sets	4 of ( 2v ), 2 of ( 2f )
rotational symmetry group	32 elements.
full symmetry group	64 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, rsr‑1sr2 >
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:{4,8|4}.

It is self-Petrie dual.

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

It can be 3-split to give R11.2′.
It can be 5-split to give R19.11′.
It can be 7-split to give R27.3′.
It can be 9-split to give R35.2′.
It can be 11-split to give R43.6′.

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

It is a member of series ι'.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is K_4,4.

Other Regular Maps

General Index

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