48 singularity types
| Singularity types | \(K^2\) | Orders of local fundamental groups |
Local indices | Index | Cascade |
|---|---|---|---|---|---|
| [8] | 25/2 | 8 | 4 | 4 | cascade |
| [2], [2], [2, 3, 2] | 9/2 | 2, 2, 8 | 1, 1, 4 | 4 | cascade |
| [2, [2], [2], [2, 3]] | 9/2 | 40 | 4 | 4 | cascade |
| [2, 2, 2, 2], [5, 5] | 15/2 | 5, 24 | 1, 4 | 4 | cascade |
| [5, 2, 2, 2, 2, 2, 5] | 13/2 | 104 | 4 | 4 | cascade |
| [2], [2], [2, 2, 3, 3, 2, 2] | 5/2 | 2, 2, 40 | 1, 1, 4 | 4 | cascade |
| [2, 2], [2, 2, 2], [2, 3, 2] | 3/2 | 3, 4, 8 | 1, 1, 4 | 4 | cascade |
| [2], [2], [2, 2], [2, [2], [2], [3]] | 3/2 | 2, 2, 3, 24 | 1, 1, 1, 4 | 4 | cascade |
| [2, 2], [2, [2], [2], [2, 2, 3]] | 3/2 | 3, 56 | 1, 4 | 4 | cascade |
| [2], [2, 2, 2, 2, 2], [2, 2, 6] | 3 | 2, 6, 16 | 1, 1, 4 | 4 | cascade |
| [2, 2], [2, 2], [2, 2, 4, 2, 2] | 3/2 | 3, 3, 24 | 1, 1, 4 | 4 | cascade |
| [2, 2, 2], [2, 2, 2], [2, 3, 2] | 1/2 | 4, 4, 8 | 1, 1, 4 | 4 | cascade |
| [2, 2, 2], [2, 3, 2], [2, 3, 2] | 1 | 4, 8, 8 | 1, 4, 4 | 4 | cascade |
| [2, 2, 2], [2, 3, 2], [3, 2, 3] | 3/2 | 4, 8, 12 | 1, 4, 2 | 4 | cascade |
| [8], [2, 2, 2, 2, 2, 2, 2, 2] | 9/2 | 8, 9 | 4, 1 | 4 | cascade |
| [2], [2], [2, 3, 2], [2, [2], [2], [2]] | 1/2 | 2, 2, 8, 8 | 1, 1, 4, 1 | 4 | cascade |
| [2], [2], [2, [2], [2], [2, 2, 2, 3]] | 1/2 | 2, 2, 72 | 1, 1, 4 | 4 | cascade |
| [2, 2, 2], [2, [2], [2], [2, 2, 3]] | 1/2 | 4, 56 | 1, 4 | 4 | cascade |
| [2, 3, 2], [2, [2], [2], [2, 2, 2]] | 1/2 | 8, 16 | 4, 1 | 4 | cascade |
| [2, [2], [2], [2, 2, 2, 2, 2, 3]] | 1/2 | 104 | 4 | 4 | cascade |
| [2, [2], [2], [2]], [2, [2], [2], [2, 3]] | 1/2 | 8, 40 | 1, 4 | 4 | cascade |
| [2, [2], [2], [3]], [2, [2], [2], [2, 2]] | 1/2 | 24, 12 | 4, 1 | 4 | cascade |
| [2], [2], [2, 2, 3, 2, 2, 3, 2, 2] | 1/2 | 2, 2, 72 | 1, 1, 4 | 4 | cascade |
| [2, 2], [2, 2, 2], [2, 2, 4, 2, 2] | 1/2 | 3, 4, 24 | 1, 1, 4 | 4 | cascade |
| [2, 3, 2], [2, 3, 2], [3, 2, 2, 3] | 1 | 8, 8, 16 | 4, 4, 2 | 4 | cascade |
| [2, 3, 2], [2, 3, 2], [2, [2], [2], [3]] | 1/2 | 8, 8, 24 | 4, 4, 4 | 4 | cascade |
| [4], [2, [2], [2], [3]], [2, [2], [2], [2, 2]] | 1/2 | 4, 24, 12 | 2, 4, 1 | 4 | cascade |
| [2], [2, 2, 2, 2, 2], [2, 2, 3, 2, 5] | 1 | 2, 6, 48 | 1, 1, 4 | 4 | cascade |
| [2], [2, 2, 2, 2, 2, 2, 2], [2, 2, 6] | 1 | 2, 8, 16 | 1, 1, 4 | 4 | cascade |
| [2], [8], [2, 2, 2, 2, 2, 2, 2, 2, 2] | 5/2 | 2, 8, 10 | 1, 4, 1 | 4 | cascade |
| [2, 2, 2], [3, 2, 3], [2, 2, 4, 2, 2] | 1/2 | 4, 12, 24 | 1, 2, 4 | 4 | cascade |
| [2, 2, 2, 2], [2, 2, 2, 2], [5, 2, 5] | 5/2 | 5, 5, 40 | 1, 1, 4 | 4 | cascade |
| [2, 2, 2, 2], [5, 2, 2, 2, 2, 2, 2, 5] | 3/2 | 5, 120 | 1, 4 | 4 | cascade |
| [2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [5, 5] | 3/2 | 6, 6, 24 | 1, 1, 4 | 4 | cascade |
| [3, 3], [2, 2, 2, 2, 2, 2, 2], [2, 2, 6] | 1 | 8, 8, 16 | 2, 1, 4 | 4 | cascade |
| [8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 3/2 | 8, 12 | 4, 1 | 4 | cascade |
| [2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 2, 5] | 1/2 | 2, 10, 40 | 1, 1, 4 | 4 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2], [5, 2, 2, 2, 5] | 1/2 | 9, 72 | 1, 4 | 4 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 5] | 1/2 | 12, 24 | 1, 4 | 4 | cascade |
| [4], [8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 3/2 | 4, 8, 12 | 2, 4, 1 | 4 | cascade |
| [5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5] | 1/2 | 200 | 4 | 4 | cascade |
| [2], [2], [8], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2]] | 1/2 | 2, 2, 8, 32 | 1, 1, 4, 1 | 4 | cascade |
| [2, 2, 2], [8], [2, [2], [2], [2, 2, 2, 2, 2, 2]] | 1/2 | 4, 8, 28 | 1, 4, 1 | 4 | cascade |
| [8], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2, 2, 2]] | 1/2 | 8, 40 | 4, 1 | 4 | cascade |
| [8], [2, [2], [2], [2]], [2, [2], [2], [2, 2, 2, 2, 2]] | 1/2 | 8, 8, 24 | 4, 1, 1 | 4 | cascade |
| [8], [2, [2], [2], [2, 2]], [2, [2], [2], [2, 2, 2, 2]] | 1/2 | 8, 12, 20 | 4, 1, 1 | 4 | cascade |
| [8], [2, [2], [2], [2, 2, 2]], [2, [2], [2], [2, 2, 2]] | 1/2 | 8, 16, 16 | 4, 1, 1 | 4 | cascade |
| [8], [8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 1 | 8, 8, 16 | 4, 4, 1 | 4 | cascade |