## Singular regular maps

We consider a regular map as "singular" if no two vertices have more than one common edge, and no two faces 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{8,3}632 / 12 / 481,1 R3.2′3
3the dual Dyck map{3,8}612 / 32 / 481,1 R3.22
3the Klein map{7,3}856 / 24 / 841,1 R3.1′3
3the dual Klein map{3,7}824 / 56 / 841,1 R3.12
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
9NN9.1′{8,3}756 / 21 / 841,1 N9.1′0
9NN9.2′{8,3}856 / 21 / 841,1 N9.2′0
9NN9.1{3,8}721 / 56 / 841,1 N9.10
9NN9.2{3,8}821 / 56 / 841,1 N9.20
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
5The Fricke-Klein map{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 C7.21
7C7.2′{7,7}48 / 8 / 281,1 C7.2′1
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
8R8.1′{8,3}8112 / 42 / 1681,1 R8.1′0
8R8.2′{8,3}14112 / 42 / 1681,1 R8.2′0
8R8.1{3,8}842 / 112 / 1681,1 R8.10
8R8.2{3,8}1442 / 112 / 1681,1 R8.20
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
9R9.17{6,6}816 / 16 / 481,1 R9.170
9R9.18{6,6}416 / 16 / 481,1 R9.180
9R9.16′{6,5}424 / 20 / 601,1 R9.16′0
9R9.16{5,6}420 / 24 / 601,1 R9.160
9R9.5′{8,4}832 / 16 / 641,1 R9.5′0
9R9.6′{8,4}432 / 16 / 641,1 R9.6′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
9R9.3′{6,4}2448 / 32 / 961,1 R9.3′0
9R9.4′{6,4}648 / 32 / 961,1 R9.4′0
9R9.3{4,6}2432 / 48 / 961,1 R9.30
9R9.4{4,6}632 / 48 / 961,1 R9.40
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
10R10.13{6,6}618 / 18 / 541,1 R10.130
10R10.14{6,6}618 / 18 / 541,1 R10.140
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
10R10.7′{6,4}1254 / 36 / 1081,1 R10.7′0
10R10.8′{6,4}1254 / 36 / 1081,1 R10.8′0
10R10.7{4,6}1236 / 54 / 1081,1 R10.70
10R10.8{4,6}1236 / 54 / 1081,1 R10.80
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