Regular maps in the orientable surface of genus 3

NameSchläfliV / F / EmV, mFnotes C&D no.imageswire-
frames
the dual Klein map{3,7}824 / 56 / 84 1,1 replete singular is a polyhedral map permutes its vertices evenly R3.120
the Klein map{7,3}856 / 24 / 84 1,1 replete singular is a polyhedral map permutes its vertices evenly R3.1′30
the dual Dyck map{3,8}612 / 32 / 48 1,1ξ°' replete singular is a polyhedral map permutes its vertices evenly R3.220
the Dyck map{8,3}632 / 12 / 48 1,1ξ° replete singular is a polyhedral map permutes its vertices evenly R3.2′30
S3:{4,6}{4,6}68 / 12 / 24 2,1 replete is not a polyhedral map permutes its vertices evenly R3.410
S3:{6,4}{6,4}612 / 8 / 24 1,2 replete is not a polyhedral map permutes its vertices evenly R3.4′20
S3:{3,12}{3,12}84 / 16 / 24 4,1 replete is not a polyhedral map permutes its vertices evenly R3.310
S3:{12,3}{12,3}816 / 4 / 24 1,4 replete is not a polyhedral map permutes its vertices evenly R3.3′10
S3:{4,8|4}{4,8}84 / 8 / 16 4,1ι replete is not a polyhedral map permutes its vertices oddly R3.510
S3:{8,4|4}{8,4}88 / 4 / 16 1,4ι' replete is not a polyhedral map permutes its vertices oddly R3.5′10
S3:{4,8|2}{4,8}84 / 8 / 16 4,2 replete is not a polyhedral map permutes its vertices oddly R3.62 3
S3:{8,4|2}{8,4}88 / 4 / 16 2,4 replete is not a polyhedral map permutes its vertices oddly R3.6′4 3
S3:{6,6}{6,6}44 / 4 / 12 2,2ν° Faces share vertices with themselves replete is not a polyhedral map permutes its vertices evenly R3.820
S3:{4,12}{4,12}62 / 6 / 12 12,2ε°' ζ'°' Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R3.74 1
S3:{12,4}{12,4}66 / 2 / 12 2,12ε° ζ'° Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R3.7′1 1
S3:{8,8}4{8,8}42 / 2 / 8 8,8η° Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R3.102 1
S3:{8,8}2{8,8}22 / 2 / 8 8,8γ° Faces share vertices with themselves trivial is not a polyhedral map permutes its vertices oddly R3.112 4
S3{7,14}{7,14}21 / 2 / 7 14,7α Faces share vertices with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly R3.910
S3:{14,7}{14,7}22 / 1 / 7 7,14α' Faces share vertices with themselves Faces share edges with themselves trivial permutes its vertices oddly R3.9′20
S3{12,12}{12,12}21 / 1 / 6 12,12β° 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 R3.121 2

Other Regular Maps

General Index

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