Regular maps in the orientable surface of genus 1

NameSchläfliV / F / EmV, mFnotes C&D no.imageswire-
frames
{4,4}(1,0){4,4}21 / 1 / 2 4,4series s Faces share vertices with themselves Faces share edges with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly R1.s1-01 2
{6,3}(1,1){6,3}22 / 1 / 3 3,6series iseries p Faces share vertices with themselves Faces share edges with themselves trivial is not a polyhedral map permutes its vertices oddly R1.t1-1′50
{3,6}(1,1){3,6}21 / 2 / 3 6,3series qseries z Faces share vertices with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly R1.t1-120
{4,4}(1,1){4,4}22 / 2 / 4 4,4series hseries jseries k Faces share vertices with themselves trivial is not a polyhedral map permutes its vertices oddly R1.s1-16 7
{4,4}(2,0){4,4}44 / 4 / 8 2,2series lseries m replete is not a polyhedral map permutes its vertices oddly R1.s2-04 8
{6,3}(0,2){6,3}66 / 3 / 9 1,3 replete is not a polyhedral map permutes its vertices oddly R1.t0-2′10
{3,6}(0,2){3,6}63 / 6 / 9 3,1 replete is not a polyhedral map permutes its vertices oddly R1.t0-230
{4,4}(2,1){4,4}105 / 5 / 10 1,1 Chiral replete singular is not a polyhedral map permutes its vertices oddly C1.s2-110
{6,3}(2,2){6,3}48 / 4 / 12 1,2 replete is not a polyhedral map permutes its vertices evenly R1.t2-2′10
{3,6}(2,2){3,6}44 / 8 / 12 2,1 replete is not a polyhedral map permutes its vertices evenly R1.t2-210
{4,4}(2,2){4,4}48 / 8 / 16 1,1 replete singular is not a polyhedral map permutes its vertices oddly R1.s2-22 2
{4,4}(3,0){4,4}69 / 9 / 18 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.s3-010
{4,4}(3,1){4,4}1010 / 10 / 20 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s3-120
{6,3}(1,3){6,3}1414 / 7 / 21 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t1-3′10
{3,6}(1,3){3,6}147 / 14 / 21 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t1-310
{4,4}(3,2){4,4}2613 / 13 / 26 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s3-210
{6,3}(3,3){6,3}618 / 9 / 27 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.t3-3′10
{3,6}(3,3){3,6}69 / 18 / 27 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t3-310
{4,4}(4,0){4,4}816 / 16 / 32 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.s4-010
{4,4}(4,1){4,4}3417 / 17 / 34 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.s4-110
{6,3}(0,4){6,3}1224 / 12 / 36 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t0-4′10
{4,4}(3,3){4,4}618 / 18 / 36 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.s3-310
{3,6}(0,4){3,6}1212 / 24 / 36 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.t0-410
{6,3}(2,4){6,3}2626 / 13 / 39 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t2-4′10
{3,6}(2,4){3,6}2613 / 26 / 39 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.t2-410
{4,4}(4,2){4,4}2020 / 20 / 40 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s4-21 2
{6,3}(4,4){6,3}832 / 16 / 48 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t4-4′10
{3,6}(4,4){3,6}816 / 32 / 48 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t4-410
{4,4}(5,0){4,4}1025 / 25 / 50 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.s5-010
{4,4}(4,3){4,4}5025 / 25 / 50 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.s4-310
{4,4}(5,1){4,4}2626 / 26 / 52 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s5-110
{6,3}(1,5){6,3}3838 / 19 / 57 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t1-5′10
{3,6}(1,5){3,6}3819 / 38 / 57 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t1-510
{4,4}(5,2){4,4}5829 / 29 / 58 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s5-210
{6,3}(3,5){6,3}4242 / 21 / 63 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t3-5′10
{3,6}(3,5){3,6}4221 / 42 / 63 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.t3-510
{4,4}(4,4){4,4}832 / 32 / 64 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.s4-410
{4,4}(5,3){4,4}3434 / 34 / 68 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s5-310
{4,4}(6,0){4,4}1236 / 36 / 72 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.s6-010
{4,4}(6,1){4,4}7437 / 37 / 74 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s6-110
{6,3}(5,5){6,3}1050 / 25 / 75 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.t5-5′10
{3,6}(5,5){3,6}1025 / 50 / 75 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t5-510
{4,4}(6,2){4,4}2040 / 40 / 80 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.s6-210
{6,3}(0,6){6,3}1854 / 27 / 81 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.t0-6′10
{3,6}(0,6){3,6}1827 / 54 / 81 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.t0-610
{4,4}(5,4){4,4}8241 / 41 / 82 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.s5-410
{6,3}(2,6){6,3}2856 / 28 / 84 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.t2-6′10
{3,6}(2,6){3,6}2828 / 56 / 84 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.t2-610
{4,4}(6,3){4,4}3045 / 45 / 90 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s6-310
{6,3}(4,6){6,3}6262 / 31 / 93 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t4-6′10
{3,6}(4,6){3,6}6231 / 62 / 93 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t4-610
{4,4}(7,0){4,4}1449 / 49 / 98 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.s7-010
{4,4}(5,5){4,4}1050 / 50 / 100 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.s5-510
{4,4}(7,1){4,4}5050 / 50 / 100 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.s7-110
{6,3}(6,6){6,3}1272 / 36 / 108 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t6-6′10
{3,6}(6,6){3,6}1236 / 72 / 108 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t6-610
{6,3}(1,7){6,3}7474 / 37 / 111 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t1-7′10
{3,6}(1,7){3,6}7437 / 74 / 111 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.t1-710
{6,3}(3,7){6,3}7878 / 39 / 117 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t3-7′10
{3,6}(3,7){3,6}7839 / 78 / 117 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t3-710
{6,3}(5,7){6,3}8686 / 43 / 129 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t5-7′10
{3,6}(5,7){3,6}8643 / 86 / 129 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t5-710
{6,3}(0,8){6,3}2496 / 48 / 144 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t0-8′10
{3,6}(0,8){3,6}2448 / 96 / 144 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t0-810
{6,3}(7,7){6,3}1498 / 49 / 147 1,1 replete singular is a polyhedral map permutes its vertices oddly R1.t7-7′10
{3,6}(7,7){3,6}1449 / 98 / 147 1,1 replete singular is a polyhedral map permutes its vertices evenly R1.t7-710
{6,3}(2,8){6,3}9898 / 49 / 147 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t2-8′10
{3,6}(2,8){3,6}9849 / 98 / 147 1,1 Chiral replete singular is a polyhedral map permutes its vertices evenly C1.t2-810

Other Regular Maps

General Index