S4:{6,6}3,2

Statistics

genus c4, orientable
Schläfli formula c{6,6}
V / F / E c 6 / 6 / 18
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 2
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6 Hamiltonian, each with 6 edges
6 double, each with 6 edges
18, each with 2 edges
6 Hamiltonian, each with 6 edges
antipodal sets3 of ( 2v ), 3 of ( 2e )
rotational symmetry group36 elements.
full symmetry group72 elements.
its presentation c< r, s, t | t2, (sr)2, (st)2, (rt)2, s6, r‑1s3r‑1s, r6 >
C&D number cR4.8′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

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

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

It can be 5-split to give R28.22′.
It can be 7-split to give R40.7′.
It can be 11-split to give R64.20′.
It can be built by 2-splitting {3,6}(0,2).

It can be triambulated to give S4:{3,12}.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 3 . 6-cycle.

Comments

This regular map appears, in a very different presentation, on page 46 of H01, where it is considered as a dessin d'enfant. The 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".


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