Regular maps in the orientable surface of genus 3

NameSchläfliV / F / EmV, mFnotesC&D no.images
S3:{3,7}{3,7}824 / 56 / 841,1 replete singular is a polyhedral map permutes its vertices evenly R3.11
the Klein map, S3:{7,3}{7,3}856 / 24 / 841,1 replete singular is a polyhedral map permutes its vertices evenly R3.1′2
S3:{3,8}{3,8}612 / 32 / 481,1 replete singular is a polyhedral map permutes its vertices evenly R3.21
the Dyck Map, S3:{8,3}{8,3}632 / 12 / 481,1 replete singular is a polyhedral map permutes its vertices evenly R3.2′2
S3:{3,12}{3,12}84 / 16 / 244,1 replete is not a polyhedral map permutes its vertices evenly R3.31
S3:{12,3}{12,3}816 / 4 / 241,4 replete is not a polyhedral map permutes its vertices evenly R3.3′1
S3:{4,6}{4,6}68 / 12 / 242,1 replete is not a polyhedral map permutes its vertices evenly R3.41
S3:{6,4}{6,4}612 / 8 / 241,2 replete is not a polyhedral map permutes its vertices evenly R3.4′2
S3:{4,8|4}{4,8}84 / 8 / 164,1 replete is not a polyhedral map permutes its vertices oddly R3.51
S3:{8,4|4}{8,4}88 / 4 / 161,4 replete is not a polyhedral map permutes its vertices oddly R3.5′1
S3:{4,8|2}{4,8}84 / 8 / 164,2series m is not a polyhedral map permutes its vertices oddly R3.62
S3:{8,4|2}{8,4}88 / 4 / 162,4series l is not a polyhedral map permutes its vertices oddly R3.6′4
S3:{4,12}{4,12}62 / 6 / 1212,2series h Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R3.72
S3:{12,4}{12,4}66 / 2 / 122,12series j Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R3.7′1
S3:{6,6}{6,6}44 / 4 / 122,2 Faces share vertices with themselves replete is not a polyhedral map permutes its vertices evenly R3.81
S3:{8,8}4{8,8}42 / 2 / 88,8 Faces share vertices with themselves is not a polyhedral map permutes its vertices oddly R3.101
S3:{8,8}2{8,8}22 / 2 / 88,8series k Faces share vertices with themselves trivial is not a polyhedral map permutes its vertices oddly R3.111
S3{7,14}{7,14}21 / 2 / 714,7series z Faces share vertices with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly R3.91
S3:{14,7}{14,7}22 / 1 / 77,14series i Faces share vertices with themselves Faces share edges with themselves trivial permutes its vertices oddly R3.9′1
S3{12,12}{12,12}21 / 1 / 612,12series 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 R3.121

Other Regular Maps

General Index

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