Regular maps in the series p

GenusNameSchläfliV / F / EmV, mFnotesC&D no.thumbnail
1{6,3}(1,1){6,3}22 / 1 / 33,6Faces share vertices with themselves Faces share edges with themselves trivial is not a polyhedral map permutes its vertices oddly R1.t1-1′
2S2:{6,6}{6,6}22 / 2 / 66,6trivial Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R2.5
4S4:{6,12}{6,12}42 / 4 / 1212,3Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R4.9
5S5:{6,15}10{6,15}102 / 5 / 1515,3Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R5.11
7S7:{6,21}{6,21}142 / 7 / 2121,3Faces share vertices with themselves is not a polyhedral map R7.8
8S8:{6,24}{6,24}82 / 8 / 2424,3Faces share vertices with themselves is not a polyhedral map R8.6

List of series of regular maps.

Links to individual series:   h   i   j   k   l   m   p   q   s   z  .

Notes

Diagrams of these regular maps use "tadpoles" to portray the surfaces.

For each regular map in this series, the two ends of a tunnel are slightly more, or slightly less, than one third of the way along the line of tunnel-mouths. If n were divisible by 3, they would have to be exactly one-third of the way along the line, so the construction does not work for genera divisible by 3.


Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |