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| genus c | 4, orientable |
| Schläfli formula c | {6,6} |
| V / F / E c | 6 / 6 / 18 |
| notes | 
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| vertex, face multiplicity c | 2, 3 |
| 6 Hamiltonian, each with 6 edges 6 Hamiltonian, each with 6 edges 6 Hamiltonian, each with 6 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. | |
Its dual is
It is self-Petrie dual.
Other regular maps in the same manifold.
If we ignore its faces and regard it as a graph, it is isomorphic to a double K3,3.
The first diagram above, with a 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".
| Orientable | |
| Non-orientable |
The images on this page are copyright © 2010 N. Wedd