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