Regular maps in the orientable surface of genus 1: the torus

There are separate pages for regular maps in the torus showing:

NameSchläfliV / F / EmV, mFnotes C&D no.imageswire-
frames
{4,4}(1,0){4,4}21 / 1 / 2 4,4β° κ° 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 3,6α' δ ξ 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 6,3α δ' ξ' 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 4,4γ° ζ'° ζ'°' μ° 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 2,2θ θ' θ° λ λ' λ° replete is not a polyhedral map permutes its vertices oddly R1.s2-04 8
{6,3}(0,2){6,3}66 / 3 / 9 1,3ο ο° replete is not a polyhedral map permutes its vertices oddly R1.t0-2′10
{3,6}(0,2){3,6}63 / 6 / 9 3,1ο' ο°' 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 1,2ξ replete is not a polyhedral map permutes its vertices evenly R1.t2-2′10
{3,6}(2,2){3,6}44 / 8 / 12 2,1ξ' replete is not a polyhedral map permutes its vertices evenly R1.t2-210
{4,4}(2,2){4,4}48 / 8 / 16 1,1μ μ' μ° replete singular is not a polyhedral map permutes its vertices oddly R1.s2-22 2
{4,4}(3,0){4,4}69 / 9 / 18 1,1κ° 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 1,1ξ ξ° replete singular is a polyhedral map permutes its vertices oddly R1.t3-3′10
{3,6}(3,3){3,6}69 / 18 / 27 1,1ξ' ξ°' replete singular is a polyhedral map permutes its vertices evenly R1.t3-310
{4,4}(4,0){4,4}816 / 16 / 32 1,1λ° 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

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |