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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 | 3, 2 |
| 6 Hamiltonian, each with 6 edges 6, each with 6 edges 18, each with 2 edges 6 Hamiltonian, each with 6 edges | |
| antipodal sets | 3 of ( 2v ), 3 of ( 2e ) |
| rotational symmetry group | 36 elements. |
| full symmetry group | 72 elements. |
| its presentation c | < r, s, t | t2, (sr)2, (st)2, (rt)2, s6, r-1s3r-1s, r6 >. |
| C&D number c | R4.8′ |
| The statistics marked c are from the published work of Professor Marston Conder. | |
Its dual is
Its Petrie dual is
It can be built by splitting
Other regular maps in the same manifold.
If we ignore its faces and regard it as a graph, it is isomorphic to a triple 6-cycle.
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".
| Orientable | |
| Non-orientable |
The image on this page is copyright © 2010 N. Wedd