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
the Heawood map{6,3}1414 / 7 / 21 1,1 Chiral replete singular is a polyhedral map permutes its vertices oddly C1.t1-3′10
the dual Heawood map{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
{4,4}(8,0){4,4}64 / 64 / 128 1,1 R1.s8-000
{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}(8,8){6,3}96 / 48 / 144 1,1 R1.t8-{8}′00
{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
{4,4}(6,6){4,4}36 / 36 / 144 1,1 R1.s6-600
{3,6}(8,8){3,6}48 / 96 / 144 1,1 R1.t8-800
{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
{4,4}(9,0){4,4}81 / 81 / 162 1,1 R1.s9-000
{4,4}(7,7){4,4}49 / 49 / 196 1,1 R1.s7-700
{4,4}(10,0){4,4}100 / 100 / 200 1,1 R1.s10-000
{6,3}(10,10){6,3}150 / 75 / 225 1,1 R1.t10-{1000
{6,3}(0,10){6,3}150 / 75 / 225 1,1 R1.t0-{10}00
{3,6}(10,10){3,6}75 / 150 / 225 1,1 R1.t10-1000
{3,6}(0,10){3,6}75 / 150 / 225 1,1 R1.t0-1000
{4,4}(11,0){4,4}121 / 121 / 242 1,1 R1.s11-000
{4,4}(8,8){4,4}64 / 64 / 256 1,1 R1.s8-800
{4,4}(12,0){4,4}144 / 144 / 288 1,1 R1.s12-000
{6,3}(12,12){6,3}216 / 108 / 324 1,1 R1.t12-{1200
{6,3}(0,12){6,3}216 / 108 / 324 1,1 R1.t0-{12}00
{4,4}(9,9){4,4}81 / 81 / 324 1,1 R1.s9-900
{3,6}(12,12){3,6}108 / 216 / 324 1,1 R1.t12-1200
{3,6}(0,12){3,6}108 / 216 / 324 1,1 R1.t0-1200
{4,4}(13,0){4,4}169 / 169 / 338 1,1 R1.s13-000
{4,4}(14,0){4,4}196 / 196 / 392 1,1 R1.s14-000
{4,4}(10,10){4,4}100 / 100 / 400 1,1 R1.s10-1000
{6,3}(14,14){6,3}294 / 147 / 441 1,1 R1.t14-{1400
{6,3}(0,14){6,3}294 / 147 / 441 1,1 R1.t0-{14}00
{3,6}(14,14){3,6}147 / 294 / 441 1,1 R1.t14-1400
{3,6}(0,14){3,6}147 / 294 / 441 1,1 R1.t0-1400
{4,4}(15,0){4,4}225 / 225 / 450 1,1 R1.s15-000
{4,4}(11,11){4,4}121 / 121 / 484 1,1 R1.s11-1100
{4,4}(16,0){4,4}256 / 256 / 512 1,1 R1.s16-000
{6,3}(16,16){6,3}384 / 192 / 576 1,1 R1.t16-{1600
{6,3}(0,16){6,3}384 / 192 / 576 1,1 R1.t0-{16}00
{4,4}(12,12){4,4}144 / 144 / 576 1,1 R1.s12-1200
{3,6}(16,16){3,6}192 / 384 / 576 1,1 R1.t16-1600
{3,6}(0,16){3,6}192 / 384 / 576 1,1 R1.t0-1600
{4,4}(13,13){4,4}169 / 169 / 676 1,1 R1.s13-1300
{4,4}(14,14){4,4}196 / 196 / 784 1,1 R1.s14-1400
{4,4}(15,15){4,4}225 / 225 / 900 1,1 R1.s15-1500
{4,4}(16,16){4,4}256 / 256 / 1024 1,1 R1.s16-1600

Other Regular Maps

General Index