|
Tetrahedron
Tet
V 4,E 6,F 4=4{3}
χ=2, group=Td, A3, (*332)
3 | 2 3
| 2 2 2 - 3.3.3
W1, U01, K06, C15
|
Octahedron |
Truncated tetrahedron
Tut
V 12,E 18,F 8=4{3}+4{6}
χ=2, group=Td, A3, (*332), order 24
2 3 | 3 - 3.6.6
W6, U02, K07, C16
|
Cuboctahedron |
Truncated octahedron |
Icosahedron |
|
Octahedron
Oct
V 6,E 12,F 8=8{3}
χ=2, group=Oh, BC3, (*432)
4 | 2 3 - 3.3.3.3
W2, U05, K10, C17
|
Hexahedron
Cube
V 8,E 12,F 6=6{4}
χ=2, group=Oh, BC3, (*432)
3 | 2 4 - 4.4.4
W3, U06, K11, C18
|
Cuboctahedron
Co
V 12,E 24,F 14=8{3}+6{4}
χ=2, group=Oh, BC3, (*432), order 48
Td, (*332), order 24
2 | 3 4
3 3 | 2 - 3.4.3.4
W11, U07, K12, C19
|
Truncated cube
Tic
V 24,E 36,F 14=8{3}+6{8}
χ=2, group=Oh, BC3, (*432), order 48
2 3 | 4 - 3.8.8
W8, U09, K14, C21
Truncated hexahedron
|
Truncated octahedron
Toe
V 24,E 36,F 14=6{4}+8{6}
χ=2, group=Oh, BC3, (*432), order 48
Th, and (*332), order 24
2 4 | 3
3 3 2 | - 4.6.6
W7, U08, K13, C20
|
Rhombicuboctahedron
Sirco
V 24,E 48,F 26=8{3}+(6+12){4}
χ=2, group=Oh, BC3, (*432), order 48
3 4 | 2 - 3.4.4.4
W13, U10, K15, C22
Rhombicuboctahedron
|
Truncated cuboctahedron
Girco
V 48,E 72,F 26=12{4}+8{6}+6{8}
χ=2, group=Oh, BC3, (*432), order 48
2 3 4 | - 4.6.8
W15, U11, K16, C23
Rhombitruncated cuboctahedron Truncated cuboctahedron
|
Snub cube
Snic
V 24,E 60,F 38=(8+24){3}+6{4}
χ=2, group=O, ½BC3, +, (432), order 24
| 2 3 4 - 3.3.3.3.4
W17, U12, K17, C24
|
|
Icosahedron
Ike
V 12,E 30,F 20=20{3}
χ=2, group=Ih, H3, (*532)
5 | 2 3 - 3.3.3.3.3
W4, U22, K27, C25
|
Dodecahedron
Doe
V 20,E 30,F 12=12{5}
χ=2, group=Ih, H3, (*532)
3 | 2 5 - 5.5.5
W5, U23, K28, C26
|
Icosidodecahedron
Id
V 30,E 60,F 32=20{3}+12{5}
χ=2, group=Ih, H3, (*532), order 120
2 | 3 5 - 3.5.3.5
W12, U24, K29, C28
|
Truncated dodecahedron
Tid
V 60,E 90,F 32=20{3}+12{10}
χ=2, group=Ih, H3, (*532), order 120
2 3 | 5 - 3.10.10
W10, U26, K31, C29
|
Truncated icosahedron
Ti
V 60,E 90,F 32=12{5}+20{6}
χ=2, group=Ih, H3, (*532), order 120
2 5 | 3 - 5.6.6
W9, U25, K30, C27
|
Rhombicosidodecahedron
Srid
V 60,E 120,F 62=20{3}+30{4}+12{5}
χ=2, group=Ih, H3, (*532), order 120
3 5 | 2 - 3.4.5.4
W14, U27, K32, C30
Rhombicosidodecahedron
|
Truncated icosidodecahedron
Grid
V 120,E 180,F 62=30{4}+20{6}+12{10}
χ=2, group=Ih, H3, (*532), order 120
2 3 5 | - 4.6.10
W16, U28, K33, C31
Rhombitruncated icosidodecahedron Truncated icosidodecahedron
|
Snub dodecahedron
Snid
V 60,E 150,F 92=(20+60){3}+12{5}
χ=2, group=I, ½H3, +, (532), order 60
| 2 3 5 - 3.3.3.3.5
W18, U29, K34, C32
|