# Polyhedron Coordination Sequences

## Platonic Solids

confignamecoordination sequenceOEIS entry
3.3.3 (V3.3.3)tetrahedron1, 3
4.4.4 (V3.3.3.3)cube
hexahedron
square prism
trigonal trapezohedron
1, 3, 3, 1
5.5.5 (V3.3.3.3.3)dodecahedron1, 3, 6, 6, 3, 1
3.3.3.3 (V4.4.4)octahedron
triangular antiprism
square bipyramid
1, 4, 1
3.3.3.3.3 (V5.5.5)icosahedron1, 5, 5, 1

## Archimedean Solids

confignamecoordination sequenceOEIS entry
3.6.6truncated tetrahedron1, 3, 4, 4
3.8.8truncated cube1, 3, 4, 6, 6, 3, 1A298808
3.10.10truncated dodecahedron1, 3, 4, 6, 8, 10, 8, 10, 6, 3, 1A298809
4.6.6truncated octahedron1, 3, 5, 6, 5, 3, 1A161435
4.6.8truncated cuboctahedron1, 3, 5, 7, 8, 8, 7, 5, 3, 1A161696
4.6.10truncated icosidodecahedron1, 3, 5, 7, 9, 11, 12, 12, 12, 12, 11, 9, 7, 5, 3, 1A162495
5.6.6truncated icosahedron1, 3, 6, 8, 10, 10, 10, 8, 3, 1A329500
3.4.3.4cuboctahedron1, 4, 6, 1
3.4a.4b.4arhombicuboctahedron1, 4, 7, 7, 4, 1
3.4.5.4rhombicosidodecahedron1, 4, 8, 11, 12, 11, 8, 4, 1A331052
3.5.3.5icosidodecahedron1, 4, 8, 8, 8, 1A330555
3a.3a.3b.3a.4
3a.3b.3a.3a.4
snub cube1, 5, 8, 7, 3
3a.3a.3b.3a.5
3a.3b.3a.3a.5
snub dodecahedron1, 5, 9, 12, 12, 11, 7, 3A331053

## Catalan Solids

confignamecoordination sequenceOEIS entry
V3.6.6triakis tetrahedron1, 3, 4
1, 6, 1

V3.8.8triakis octahedron1, 3, 9, 1
1, 8, 5

V3.10.10triakis icosahedron1, 3, 15, 12, 1
1, 10, 15, 6
A329770
A329772
V4.6.6tetrakis hexahedron1, 4, 8, 1
1, 6, 6, 1

V4.6.8disdyakis dodecahedron1, 4, 12, 8, 1
1, 6, 12, 6, 1
1, 8, 8, 8, 1
A331054
(A331054)
(A331054)
V4.6.10disdyakis triacontahedron1, 4, 16, 16, 16, 8, 1
1, 6, 18, 12, 18, 6, 1
1, 10, 10, 20, 10, 10, 1
A331055
A331056
A331057
V5.6.6pentakis dodecahedron1, 5, 10, 10, 5, 1
1, 6, 9, 9, 6, 1
(A330564)
A330564
V3.4.3.4rhombic dodecahedron1, 3, 6, 3, 1
1, 4, 4, 4, 1

V3.4a.4b.4adeltoidal icositetrahedron1, 3, 6, 6, 6, 3, 1
1, 4, 6, 8, 5, 2
1, 4, 8, 8, 5
A331058
A331059
(A331059)
V3.4.5.4deltoidal hexecontahedron1, 3, 6, 9, 12, 15, 12, 3, 1
1, 4, 8, 12, 16, 14, 5, 2
1, 5, 10, 15, 15, 10, 6
A331060
A331061
A331062
V3.5.3.5rhombic triacontahedron1, 3, 9, 6, 9, 3, 1
1, 5, 5, 10, 5, 5, 1
A331063
A331064
V3a.3a.3b.3a.4
V3a.3b.3a.3a.4
pentagonal icositetrahedron1, 3, 6, 9, 9, 6, 3, 1
1, 3, 7, 9, 8, 7, 3
1, 4, 8, 8, 8, 8, 1
A331065
A331066
A331067
V3a.3a.3b.3a.5
V3a.3b.3a.3a.5
pentagonal hexecontahedron1, 3, 6, 12, 15, 12, 15, 18, 6, 3, 1
1, 3, 8, 12, 13, 16, 17, 12, 7, 3
1, 5, 10, 10, 15, 20, 10, 10, 10, 1
A331068
A331069
A331070