## Singular regular maps

We consider a regular map as "singular" if no two vertices have more than one common edge, and no two facces have more than one common edge. This page lists singular regular maps of genus up to 11, omitting those of genus 1.

GenusNameSchläfliV / F / EmV, mFnotesC&D no.images
0the tetrahedron{3,3}44 / 4 / 61,1 R0.11
0the cube{4,3}68 / 6 / 121,1 R0.2′1
0the octahedron{3,4}66 / 8 / 121,1 R0.21
0the dodecahedron{5,3}1020 / 12 / 301,1 R0.3′1
0the icosahedron{3,5}1012 / 20 / 301,1 R0.31
5NC5:{5,5}{5,5}36 / 6 / 151,1 N5.32
5NC5:{5,4}{5,4}615 / 12 / 301,1 N5.1′1
5NC5:{4,5}{4,5}612 / 15 / 301,1 N5.11
3the Dyck Map, S3:{8,3}{8,3}632 / 12 / 481,1 R3.2′3
3S3:{3,8}{3,8}612 / 32 / 481,1 R3.22
3the Klein map, S3:{7,3}{7,3}856 / 24 / 841,1 R3.1′2
3S3:{3,7}{3,7}824 / 56 / 841,1 R3.11
6NC6:{5,4}{5,4}520 / 16 / 401,1 N6.3′1
6NC6:{4,5}{4,5}516 / 20 / 401,1 N6.31
7NC7:{6,4}{6,4}515 / 10 / 301,1 N7.1′1
7NC7:{4,6}{4,6}510 / 15 / 301,1 N7.11
4S4:{5,5}{5,5}612 / 12 / 301,1 R4.62
4S4:{6,4}{6,4}418 / 12 / 361,1 R4.3′1
4S4:{4,6}{4,6}412 / 18 / 361,1 R4.31
4S4:{5,4}{5,4}630 / 24 / 601,1 R4.2′1
4S4:{4,5}{4,5}624 / 30 / 601,1 R4.21
8NN8.1′{7,3}984 / 36 / 1261,1 N8.1′0
8NN8.1{3,7}936 / 84 / 1261,1 N8.10
9NN9.2′{8,3}856 / 21 / 841,1 N9.2′0
9NN9.1′{8,3}756 / 21 / 841,1 N9.1′0
9NN9.2{3,8}821 / 56 / 841,1 N9.20
9NN9.1{3,8}721 / 56 / 841,1 N9.10
5S5:{5,5}{5,5}416 / 16 / 401,1 R5.90
5S5:{6,4}{6,4}1224 / 16 / 481,1 R5.4′0
5S5:{4,6}{4,6}1216 / 24 / 481,1 R5.40
5S5:{5,4}{5,4}1040 / 32 / 801,1 R5.3′0
5S5:{4,5}{4,5}1032 / 40 / 801,1 R5.30
5S5:{8,3}{8,3}1264 / 24 / 961,1 R5.1′0
5S5:{3,8}{3,8}1224 / 64 / 961,1 R5.10
10NN10.6′{6,5}412 / 10 / 301,1 N10.6′0
10NN10.6{5,6}410 / 12 / 301,1 N10.60
10NN10.1′{6,4}624 / 16 / 481,1 N10.1′0
10NN10.1{4,6}616 / 24 / 481,1 N10.10
11NC11:{6,6}{6,6}39 / 9 / 271,1 N11.21
11NC11:{6,4}{6,4}1227 / 18 / 541,1 N11.1′1
11NC11:{4,6}{4,6}1218 / 27 / 541,1 N11.11
6S6:{6,4}{6,4}1030 / 20 / 601,1 R6.2′1
6S6:{4,6}{4,6}1020 / 30 / 601,1 R6.21
6S6:{10,3}{10,3}650 / 15 / 751,1 R6.1′0
6S6:{3,10}{3,10}615 / 50 / 751,1 R6.10
12NC12{6,4}5{6,4}530 / 20 / 601,1 N12.1′1
12NN12.2′{6,4}1030 / 20 / 601,1 N12.2′0
12NC12{4,6}5{4,6}520 / 30 / 601,1 N12.11
12NN12.2{4,6}1020 / 30 / 601,1 N12.20
7C7.2′{7,7}48 / 8 / 281,1 C7.2′1
7C7.2{7,7}48 / 8 / 281,1 C7.21
7S7:{7,3}{7,3}18168 / 72 / 2521,1 R7.1′0
7S7:{3,7}{3,7}1872 / 168 / 2521,1 R7.10
14NN14.1′{10,3}1560 / 18 / 901,1 N14.1′0
14NN14.1{3,10}1518 / 60 / 901,1 N14.10
15NN15.1′{7,3}13182 / 78 / 2731,1 N15.1′0
15NN15.1{3,7}1378 / 182 / 2731,1 N15.10
8R8.2′{8,3}14112 / 42 / 1681,1 R8.2′0
8R8.1′{8,3}8112 / 42 / 1681,1 R8.1′0
8R8.2{3,8}1442 / 112 / 1681,1 R8.20
8R8.1{3,8}842 / 112 / 1681,1 R8.10
16NN16.2′{6,4}842 / 28 / 841,1 N16.2′0
16NN16.2{4,6}828 / 42 / 841,1 N16.20
16NN16.1′{9,3}784 / 28 / 1261,1 N16.1′0
16NN16.1{3,9}728 / 84 / 1261,1 N16.10
17NN17.1′{8,3}10120 / 45 / 1801,1 N17.1′0
17NN17.1{3,8}1045 / 120 / 1801,1 N17.10
9R9.18{6,6}416 / 16 / 481,1 R9.180
9R9.17{6,6}816 / 16 / 481,1 R9.170
9R9.16′{6,5}424 / 20 / 601,1 R9.16′0
9R9.16{5,6}420 / 24 / 601,1 R9.160
9R9.6′{8,4}432 / 16 / 641,1 R9.6′0
9R9.5′{8,4}832 / 16 / 641,1 R9.5′0
9R9.5{4,8}816 / 32 / 641,1 R9.50
9R9.6{4,8}416 / 32 / 641,1 R9.60
9R9.14{5,5}832 / 32 / 801,1 R9.140
9R9.4′{6,4}648 / 32 / 961,1 R9.4′0
9R9.3′{6,4}2448 / 32 / 961,1 R9.3′0
9R9.4{4,6}632 / 48 / 961,1 R9.40
9R9.3{4,6}2432 / 48 / 961,1 R9.30
9R9.2′{5,4}2080 / 64 / 1601,1 R9.2′0
9R9.2{4,5}2064 / 80 / 1601,1 R9.20
10C10.3{8,8}69 / 9 / 361,1 C10.30
10R10.14{6,6}618 / 18 / 541,1 R10.140
10R10.13{6,6}618 / 18 / 541,1 R10.130
10C10.2′{8,4}836 / 18 / 721,1 C10.2′0
10C10.2{4,8}818 / 36 / 721,1 C10.20
10R10.9′{7,4}842 / 24 / 841,1 R10.9′0
10R10.9{4,7}824 / 42 / 841,1 R10.90
10R10.2′{12,3}672 / 18 / 1081,1 R10.2′0
10R10.8′{6,4}1254 / 36 / 1081,1 R10.8′0
10R10.7′{6,4}1254 / 36 / 1081,1 R10.7′0
10R10.8{4,6}1236 / 54 / 1081,1 R10.80
10R10.7{4,6}1236 / 54 / 1081,1 R10.70
10R10.2{3,12}618 / 72 / 1081,1 R10.20
10R10.1′{9,3}12108 / 36 / 1621,1 R10.1′0
10R10.1{3,9}1236 / 108 / 1621,1 R10.10
10R10.6′{5,4}890 / 72 / 1801,1 R10.6′0
10R10.6{4,5}872 / 90 / 1801,1 R10.60
10C10.1′{8,3}12144 / 54 / 2161,1 C10.1′0
10C10.1{3,8}1254 / 144 / 2161,1 C10.10
11R11.5{6,6}620 / 20 / 601,1 R11.50
11R11.1′{6,4}1060 / 40 / 1201,1 R11.1′0
11R11.1{4,6}1040 / 60 / 1201,1 R11.10
22NN22.4′{8,6}316 / 12 / 481,1 N22.4′0
22NN22.4{6,8}312 / 16 / 481,1 N22.40