Hurwitz regular maps
A theorem by Hurwitz
implies that the number of edges of a regular map of genus >1 cannot exceed (-42 * the Euler characteristic of
its embedding manifold). This page lists those regular maps (of Euler characteristic up to 200) that attain
this limit. The three of orientable genus 14 form the
Hurwitz triplet.
| Genus | Name | Schläfli | V / F / E | mV, mF | notes | C&D no. | images |
|---|
| 3 | the Klein map | {7,3}8 | 56 / 24 / 84 | 1,1 |     | R3.1′ | 3 |
| 3 | the dual Klein map | {3,7}8 | 24 / 56 / 84 | 1,1 | | R3.1 | 2 |
| 8N | N8.1′ | {7,3}9 | 84 / 36 / 126 | 1,1 | | N8.1′ | 0 |
| 8N | N8.1 | {3,7}9 | 36 / 84 / 126 | 1,1 | | N8.1 | 0 |
| 7 | S7:{7,3} | {7,3}18 | 168 / 72 / 252 | 1,1 | | R7.1′ | 0 |
| 7 | S7:{3,7} | {3,7}18 | 72 / 168 / 252 | 1,1 | | R7.1 | 0 |
| 15N | N15.1′ | {7,3}13 | 182 / 78 / 273 | 1,1 | | N15.1′ | 0 |
| 15N | N15.1 | {3,7}13 | 78 / 182 / 273 | 1,1 | | N15.1 | 0 |
| 14 | R14.3′ | {7,3}14 | 364 / 156 / 546 | 1,1 | | R14.3′ | 0 |
| 14 | R14.2′ | {7,3}26 | 364 / 156 / 546 | 1,1 | | R14.2′ | 0 |
| 14 | R14.1′ | {7,3}12 | 364 / 156 / 546 | 1,1 | | R14.1′ | 0 |
| 14 | R14.1 | {3,7}12 | 156 / 364 / 546 | 1,1 | | R14.1 | 0 |
| 14 | R14.2 | {3,7}26 | 156 / 364 / 546 | 1,1 | | R14.2 | 0 |
| 14 | R14.3 | {3,7}14 | 156 / 364 / 546 | 1,1 | | R14.3 | 0 |
| 17 | C17.1′ | {7,3}16 | 448 / 192 / 672 | 1,1 |  | C17.1′ | 0 |
| 17 | C17.1 | {3,7}16 | 192 / 448 / 672 | 1,1 | | C17.1 | 0 |
| 147N | N147.1′ | {7,3}15 | 2030 / 870 / 3045 | 1,1 | | N147.1′ | 0 |
| 147N | N147.1 | {3,7}15 | 870 / 2030 / 3045 | 1,1 | | N147.1 | 0 |
Other Regular Maps
General Index