S4:{6,6}2,3

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 c2, 3
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
6 Hamiltonian, each with 6 edges
6 Hamiltonian, each with 6 edges
6 Hamiltonian, each with 6 edges
18, each with 2 edges
antipodal sets3 of ( 2f ), 3 of ( 2e, 2h3 )
rotational symmetry group36 elements.
full symmetry group72 elements.
its presentation c< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, s‑1r3s‑1r, s6 >
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}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 . K3,3.

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".


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