S4:{6,6}2,3

Statistics

genus c	4, orientable
Schläfli formula c	{6,6}
V / F / E c	6 / 6 / 18
notes
vertex, face multiplicity c	2, 3
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	6, each with 6 edges 6, each with 6 edges 6, each with 6 edges 18, each with 2 edges 18, each with 2 edges
antipodal sets	3 of ( 2f ), 3 of ( 2e, 2h3 )
rotational symmetry group	36 elements.
full symmetry group	72 elements.
its presentation c	< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, s‑1r3s‑1r, s6 >
C&D number c	R4.8
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{6,6}3,2.

It is self-Petrie dual.

It can be derived by stellation (with path <1,-1;-1,1>) from {6,3}_(0,2). The density of the stellation is 4.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 2 . K_3,3.

Comments

The second diagram above, with one hexagonal "hole" in its centre, was derived from the diagram of its dual on page 46 of ^H01, where it is considered as a dessin d'enfant. That graph is bipartite, and the actions of the dessin act on the edges of the graph to generate S3×C3. The authors obtained it by a method they term "origami".

Other Regular Maps

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