| config | name | coordination sequence | OEIS entry |
|---|---|---|---|
| 3.3.3 (V3.3.3) | tetrahedron | 1, 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) | dodecahedron | 1, 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) | icosahedron | 1, 5, 5, 1 |
| config | name | coordination sequence | OEIS entry |
|---|---|---|---|
| 3.6.6 | truncated tetrahedron | 1, 3, 4, 4 | |
| 3.8.8 | truncated cube | 1, 3, 4, 6, 6, 3, 1 | A298808 |
| 3.10.10 | truncated dodecahedron | 1, 3, 4, 6, 8, 10, 8, 10, 6, 3, 1 | A298809 |
| 4.6.6 | truncated octahedron | 1, 3, 5, 6, 5, 3, 1 | A161435 |
| 4.6.8 | truncated cuboctahedron | 1, 3, 5, 7, 8, 8, 7, 5, 3, 1 | A161696 |
| 4.6.10 | truncated icosidodecahedron | 1, 3, 5, 7, 9, 11, 12, 12, 12, 12, 11, 9, 7, 5, 3, 1 | A162495 |
| 5.6.6 | truncated icosahedron | 1, 3, 6, 8, 10, 10, 10, 8, 3, 1 | A329500 |
| 3.4.3.4 | cuboctahedron | 1, 4, 6, 1 | |
| 3.4a.4b.4a | rhombicuboctahedron | 1, 4, 7, 7, 4, 1 | |
| 3.4.5.4 | rhombicosidodecahedron | 1, 4, 8, 11, 12, 11, 8, 4, 1 | A331052 |
| 3.5.3.5 | icosidodecahedron | 1, 4, 8, 8, 8, 1 | A330555 |
| 3a.3a.3b.3a.4 3a.3b.3a.3a.4 | snub cube | 1, 5, 8, 7, 3 | |
| 3a.3a.3b.3a.5 3a.3b.3a.3a.5 | snub dodecahedron | 1, 5, 9, 12, 12, 11, 7, 3 | A331053 |
| config | name | coordination sequence | OEIS entry |
|---|---|---|---|
| V3.6.6 | triakis tetrahedron | 1, 3, 4 1, 6, 1 | |
| V3.8.8 | triakis octahedron | 1, 3, 9, 1 1, 8, 5 | |
| V3.10.10 | triakis icosahedron | 1, 3, 15, 12, 1 1, 10, 15, 6 | A329770 A329772 |
| V4.6.6 | tetrakis hexahedron | 1, 4, 8, 1 1, 6, 6, 1 | |
| V4.6.8 | disdyakis dodecahedron | 1, 4, 12, 8, 1 1, 6, 12, 6, 1 1, 8, 8, 8, 1 | A331054 (A331054) (A331054) |
| V4.6.10 | disdyakis triacontahedron | 1, 4, 16, 16, 16, 8, 1 1, 6, 18, 12, 18, 6, 1 1, 10, 10, 20, 10, 10, 1 | A331055 A331056 A331057 |
| V5.6.6 | pentakis dodecahedron | 1, 5, 10, 10, 5, 1 1, 6, 9, 9, 6, 1 | (A330564) A330564 |
| V3.4.3.4 | rhombic dodecahedron | 1, 3, 6, 3, 1 1, 4, 4, 4, 1 | |
| V3.4a.4b.4a | deltoidal icositetrahedron | 1, 3, 6, 6, 6, 3, 1 1, 4, 6, 8, 5, 2 1, 4, 8, 8, 5 | A331058 A331059 (A331059) |
| V3.4.5.4 | deltoidal hexecontahedron | 1, 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 |
| V3.5.3.5 | rhombic triacontahedron | 1, 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 icositetrahedron | 1, 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 hexecontahedron | 1, 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 |