## 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.

GenusNameSchläfliV / F / EmV, mFnotesC&D no.images
3the Klein map{7,3}856 / 24 / 841,1 R3.1′2
3the dual Klein map{3,7}824 / 56 / 841,1 R3.11
8NN8.1′{7,3}984 / 36 / 1261,1 N8.1′0
8NN8.1{3,7}936 / 84 / 1261,1 N8.10
7S7:{7,3}{7,3}18168 / 72 / 2521,1 R7.1′0
7S7:{3,7}{3,7}1872 / 168 / 2521,1 R7.10
15NN15.1′{7,3}13182 / 78 / 2731,1 N15.1′0
15NN15.1{3,7}1378 / 182 / 2731,1 N15.10
14R14.3′{7,3}14364 / 156 / 5461,1 R14.3′0
14R14.2′{7,3}26364 / 156 / 5461,1 R14.2′0
14R14.1′{7,3}12364 / 156 / 5461,1 R14.1′0
14R14.1{3,7}12156 / 364 / 5461,1 R14.10
14R14.3{3,7}14156 / 364 / 5461,1 R14.30
14R14.2{3,7}26156 / 364 / 5461,1 R14.20
17C17.1′{7,3}16448 / 192 / 6721,1 C17.1′0
17C17.1{3,7}16192 / 448 / 6721,1 C17.10
147NN147.1′{7,3}152030 / 870 / 30451,1 N147.1′0
147NN147.1{3,7}15870 / 2030 / 30451,1 N147.10