Regular maps in the orientable surface of genus 0

NameSchläfliV / F / EmV, mFnotesC&D no.images
the tetrahedron{3,3}44 / 4 / 61,1 replete singular is a polyhedral map permutes its vertices evenly R0.11
the cube{4,3}68 / 6 / 121,1 replete singular is a polyhedral map permutes its vertices evenly R0.2′1
the octahedron{3,4}66 / 8 / 121,1 replete singular is a polyhedral map permutes its vertices oddly R0.21
the dodecahedron{5,3}1020 / 12 / 301,1 replete singular is a polyhedral map permutes its vertices evenly R0.3′1
the icosahedron{3,5}1012 / 20 / 301,1 replete singular is a polyhedral map permutes its vertices evenly R0.31
the monodigon{2,1}22 / 1 / 11,2series i Vertices with < 3 edges Faces with < 3 edges Faces share vertices with themselves Faces share edges with themselves trivial is not a polyhedral map permutes its vertices oddly R0.n11
the dimonogon{1,2}21 / 2 / 12,1series z Vertices with < 3 edges Faces with < 3 edges Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly R0.n1′2
the 2-hosohedron{2,2}2 / 2 / 22,2series k Faces with < 3 edges Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n21
the di-triangle{3,2}63 / 2 / 31,3 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n3′1
the 3-hosohedron{2,3}62 / 3 / 33,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n31
the di-square{4,2}44 / 2 / 41,4series m Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n4′1
the 4-hosohedron{2,4}42 / 4 / 44,1series l Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n42
the di-pentagon{5,2}105 / 2 / 51,5 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices evenly R0.n5′1
the 5-hosohedron{2,5}102 / 5 / 55,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n51
the di-hexagon{6,2}66 / 2 / 61,6 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n6′1
the 6-hosohedron{2,6}62 / 6 / 66,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n61
the di-heptagon{7,2}147 / 2 / 71,7 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n7′1
the 7-hosohedron{2,7}142 / 7 / 77,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n71
the di-octagon{8,2}88 / 2 / 81,8 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n8′1
the 8-hosohedron{2,8}82 / 8 / 88,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n81
the di-nonagon{9,2}189 / 2 / 91,9 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices evenly R0.n9′1
the 9-hosohedron{2,9}182 / 9 / 99,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n91
the di-decagon{10,2}1010 / 2 / 101,10 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n10′1
the 10-hosohedron{2,10}102 / 10 / 1010,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n101
the di-11-gon{11,2}2211 / 2 / 111,11 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n11′1
the 11-hosohedron{2,11}222 / 11 / 1111,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n111
the di-dodecagon{12,2}1212 / 2 / 121,12 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n12′1
the 12-hosohedron{2,12}122 / 12 / 1212,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n121
the di-13gon{13,2}2613 / 2 / 131,13 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices evenly R0.n13′1
the 13-hosohedron{2,13}262 / 13 / 1313,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n131
the di-14gon{14,2}1414 / 2 / 141,14 Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n14′1
the 14-hosohedron{2,14}142 / 14 / 1414,1 Faces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly R0.n141
the edgeless map{0,0}1 / 1 / 00,0series s Vertices with < 3 edges Faces with < 3 edges is not a polyhedral map trivial permutes its vertices evenly R0.01

Other Regular Maps

General Index

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