12 basic regular quotient singularity types and
14 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [16] | 8 |
| [11, 3] | 8 |
| [2, 5, 2] | 8 |
| [3, 6, 3] | 8 |
| [10, 3, 2] | 8 |
| [3, 5, 3, 2] | 8 |
| [2, 3, 4, 3, 2] | 8 |
| [4, 2, 2, 2, 2] | 8 |
| [2, 4, 2, 2, 2, 2, 2] | 8 |
| [10, 2, 2, 2, 2, 2, 2] | 8 |
| [3, 5, 2, 2, 2, 2, 2, 2] | 8 |
| [2, 3, 4, 2, 2, 2, 2, 2, 2] | 8 |
| [2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2] | 8 |
| [2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 8 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [9, 9] | [9, 2, 9] | [9, 2, 2, 9] | 8 |
| [9, 4, 3] | [9, 2, 4, 3] | [9, 2, 2, 4, 3] | 8 |
| [2, [2], [2], [5]] | [2, [2], [2], [2, 5]] | [2, [2], [2], [2, 2, 5]] | 8 |
| [3, 4, 4, 3] | [3, 4, 2, 4, 3] | [3, 4, 2, 2, 4, 3] | 8 |
| [9, 3, 3, 2] | [9, 2, 3, 3, 2] | [9, 2, 2, 3, 3, 2] | 8 |
| [3, 4, 3, 3, 2] | [3, 4, 2, 3, 3, 2] | [3, 4, 2, 2, 3, 3, 2] | 8 |
| [3, [2], [2], [2, 2]] | [2, [2], [2], [3, 2, 2]] | [2, [2], [2], [2, 3, 2, 2]] | 8 |
| [2, 3, 3, 3, 3, 2] | [2, 3, 3, 2, 3, 3, 2] | [2, 3, 3, 2, 2, 3, 3, 2] | 8 |
| [9, 3, 2, 2, 2, 2, 2, 2] | [9, 2, 3, 2, 2, 2, 2, 2, 2] | [9, 2, 2, 3, 2, 2, 2, 2, 2, 2] | 8 |
| [3, 4, 3, 2, 2, 2, 2, 2, 2] | [3, 4, 2, 3, 2, 2, 2, 2, 2, 2] | [3, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2] | 8 |
| [2, 3, 3, 3, 2, 2, 2, 2, 2, 2] | [2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2] | [2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2] | 8 |
| [2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2] | 8 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87