S3:{6,4}

Statistics

genus c	3, orientable
Schläfli formula c	{6,4}
V / F / E c	12 / 8 / 24
notes
vertex, face multiplicity c	1, 2
Petrie polygons holes 2nd-order Petrie polygons	8, each with 6 edges 12, each with 4 edges 12, each with 4 edges
antipodal sets	3 of ( 4v ), 4 of ( 2f ), 12 of ( 2e )
rotational symmetry group	48 elements.
full symmetry group	96 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, (sr‑2)2, r6 >
C&D number c	R3.4′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S3:{4,6}.

It is self-Petrie dual.

It is a 2-fold cover of N4:{6,4}₃.
It is a 2-fold cover of N4:{6,4}₆.
It is a 2-fold cover of S2:{6,4}.

It can be 5-split to give R27.1′.
It can be 7-split to give R39.1′.
It can be 11-split to give R63.1′.
It can be built by 2-splitting the octahedron.

It can be rectified to give rectification of S3:{6,4}.
It is the result of rectifying S3:{6,6}.

It can be triambulated to give the dual Dyck map.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is C4 × K₃.

Other Regular Maps

General Index

The images on this page are copyright © 2010 N. Wedd