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, S3:{7,3}{7,3}856 / 24 / 841,1 replete singular is a polyhedral map permutes its vertices evenly R3.1′2
3S3:{3,7}{3,7}824 / 56 / 841,1 replete singular is a polyhedral map permutes its vertices evenly R3.11
8NN8.1′{7,3}984 / 36 / 1261,1 replete singular N8.1′0
8NN8.1{3,7}936 / 84 / 1261,1 replete singular N8.10
7S7:{7,3}{7,3}18168 / 72 / 2521,1 replete singular R7.1′0
7S7:{3,7}{3,7}1872 / 168 / 2521,1 replete singular R7.10
15NN15.1′{7,3}13182 / 78 / 2731,1 replete singular N15.1′0
15NN15.1{3,7}1378 / 182 / 2731,1 replete singular N15.10
14R14.2′{7,3}26364 / 156 / 5461,1 replete singular R14.2′0
14R14.1′{7,3}12364 / 156 / 5461,1 replete singular R14.1′0
14R14.3′{7,3}14364 / 156 / 5461,1 replete singular R14.3′0
14R14.3{3,7}14156 / 364 / 5461,1 replete singular R14.30
14R14.2{3,7}26156 / 364 / 5461,1 replete singular R14.20
14R14.1{3,7}12156 / 364 / 5461,1 replete singular R14.10
17C17.1′{7,3}16448 / 192 / 6721,1 replete singular Chiral C17.1′0
17C17.1{3,7}16192 / 448 / 6721,1 replete singular Chiral C17.10
147NN147.1′{7,3}152030 / 870 / 30451,1 replete singular N147.1′0
147NN147.1{3,7}15870 / 2030 / 30451,1 replete singular N147.10

Other Regular Maps

General Index