S4:{6,4}

Statistics

genus c	4, orientable
Schläfli formula c	{6,4}
V / F / E c	18 / 12 / 36
notes
vertex, face multiplicity c	1, 1
Petrie polygons holes 2nd-order Petrie polygons	18, each with 4 edges 12, each with 6 edges 12, each with 6 edges
antipodal sets	9 of ( 2v ), 6 of ( 2f ), 18 of ( 2e ), 9 of ( 2p ), 6 of ( 2h )
rotational symmetry group	72 elements.
full symmetry group	144 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, r6, rsr‑1s2r‑1sr >
C&D number c	R4.3′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{4,6}.

Its Petrie dual is {4,4}_(3,3).

It is a 2-fold cover of C5:{6,4}.

It can be 5-split to give R40.1′.
It can be 7-split to give R58.1′.
It can be 11-split to give R94.2′.

It is the result of rectifying S4:{6,6}3,3.

List of regular maps in orientable genus 4.

Wireframe construction

	×	{6,3}(0,2)	w09:3, C.Séquin

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 1:50 seconds from the start. It is shown as a "wireframe diagram", on K_3,3. The wireframe is arranged as the skeleton of {6,3}_(0,2).

Other Regular Maps

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