80 singularity types
| Singularity types | \(K^2\) | Orders of local fundamental groups |
Local indices | Index | Cascade |
|---|---|---|---|---|---|
| [3] | 25/3 | 3 | 3 | 3 | cascade |
| [6] | 32/3 | 6 | 3 | 3 | cascade |
| [2], [2, 5] | 8 | 2, 9 | 1, 3 | 3 | cascade |
| [3], [2, 2, 2] | 16/3 | 3, 4 | 3, 1 | 3 | cascade |
| [2], [2], [2, 4, 2] | 16/3 | 2, 2, 12 | 1, 1, 3 | 3 | cascade |
| [2], [2, 3, 2, 4] | 6 | 2, 27 | 1, 3 | 3 | cascade |
| [2, 2, 2], [4, 4] | 20/3 | 4, 15 | 1, 3 | 3 | cascade |
| [2, [2], [2], [2, 4]] | 16/3 | 84 | 3 | 3 | cascade |
| [2], [3], [2, 2, 2, 2] | 10/3 | 2, 3, 5 | 1, 3, 1 | 3 | cascade |
| [2, 2, 2, 2], [2, 5] | 5 | 5, 9 | 1, 3 | 3 | cascade |
| [2, 3, 2, 2, 3, 2] | 13/3 | 39 | 3 | 3 | cascade |
| [4, 2, 2, 2, 2, 4] | 17/3 | 51 | 3 | 3 | cascade |
| [2], [2], [2, 3, 2, 3, 2] | 10/3 | 2, 2, 30 | 1, 1, 3 | 3 | cascade |
| [2], [2, 2, 2], [2, 3, 4] | 4 | 2, 4, 18 | 1, 1, 3 | 3 | cascade |
| [3], [2, 2, 2, 2, 2, 2] | 7/3 | 3, 7 | 3, 1 | 3 | cascade |
| [3], [3], [2, 2, 2, 2, 2] | 8/3 | 3, 3, 6 | 3, 3, 1 | 3 | cascade |
| [6], [2, 2, 2, 2, 2, 2] | 14/3 | 6, 7 | 3, 1 | 3 | cascade |
| [2], [2], [2], [3, [2], [2], [2]] | 8/3 | 2, 2, 2, 24 | 1, 1, 1, 3 | 3 | cascade |
| [2], [2, [2], [2], [2, 3, 2]] | 8/3 | 2, 96 | 1, 3 | 3 | cascade |
| [2], [2, 3, 2, 2, 2, 2, 4] | 3 | 2, 54 | 1, 3 | 3 | cascade |
| [2], [2], [3], [2, [2], [2], [2, 2]] | 4/3 | 2, 2, 3, 12 | 1, 1, 3, 1 | 3 | cascade |
| [3], [2, 2, 2], [2, [2], [2], [2]] | 4/3 | 3, 4, 8 | 3, 1, 1 | 3 | cascade |
| [3], [2, [2], [2], [2, 2, 2, 2]] | 4/3 | 3, 20 | 3, 1 | 3 | cascade |
| [2], [2], [2, 3, 2, 2, 2, 3, 2] | 4/3 | 2, 2, 48 | 1, 1, 3 | 3 | cascade |
| [2], [2, 2, 2], [2, 3, 2, 2, 4] | 2 | 2, 4, 36 | 1, 1, 3 | 3 | cascade |
| [2], [3], [2, 2], [2, 2, 2, 2, 2] | 1/3 | 2, 3, 3, 6 | 1, 3, 1, 1 | 3 | cascade |
| [2], [3], [2, 2, 2, 2, 2, 2, 2] | 1/3 | 2, 3, 8 | 1, 3, 1 | 3 | cascade |
| [2], [6], [2, 2, 2, 2, 2, 2, 2] | 8/3 | 2, 6, 8 | 1, 3, 1 | 3 | cascade |
| [2, 2], [2, 2, 2, 2, 2], [2, 5] | 2 | 3, 6, 9 | 1, 1, 3 | 3 | cascade |
| [2, 2, 2], [2, 2, 2], [2, 4, 2] | 4/3 | 4, 4, 12 | 1, 1, 3 | 3 | cascade |
| [2, 2, 2], [2, 2, 2], [4, 2, 4] | 8/3 | 4, 4, 24 | 1, 1, 3 | 3 | cascade |
| [3], [2, 2, 2, 2], [2, 2, 2, 2] | 1/3 | 3, 5, 5 | 3, 1, 1 | 3 | cascade |
| [3], [2, 2, 2, 2, 2, 2, 2, 2] | 1/3 | 3, 9 | 3, 1 | 3 | cascade |
| [2], [2], [2], [2, [2], [2], [2, 3, 2]] | 2/3 | 2, 2, 2, 96 | 1, 1, 1, 3 | 3 | cascade |
| [2], [2], [2, 2, 2], [2, [2], [2], [4]] | 4/3 | 2, 2, 4, 48 | 1, 1, 1, 3 | 3 | cascade |
| [2], [2, 2, 2], [2, [2], [2], [3, 2]] | 2/3 | 2, 4, 60 | 1, 1, 3 | 3 | cascade |
| [2], [2, [2], [2], [2, 2, 2, 3, 2]] | 2/3 | 2, 168 | 1, 3 | 3 | cascade |
| [2], [3], [2, [2], [2, 2], [2, 2, 2]] | 1/3 | 2, 3, 48 | 1, 3, 1 | 3 | cascade |
| [2], [3], [3], [2, [2], [2, 2], [2, 2]] | 2/3 | 2, 3, 3, 24 | 1, 3, 3, 1 | 3 | cascade |
| [2, 2, 2], [2, [2], [2], [2, 2, 4]] | 4/3 | 4, 120 | 1, 3 | 3 | cascade |
| [3], [2, 2], [2, [2], [2, 2], [2, 2]] | 1/3 | 3, 3, 24 | 3, 1, 1 | 3 | cascade |
| [3], [2, 2, 2], [2, [2], [2], [2, 2]] | 1/3 | 3, 4, 12 | 3, 1, 1 | 3 | cascade |
| [3], [2, [2], [2], [2, 2, 2, 2, 2]] | 1/3 | 3, 24 | 3, 1 | 3 | cascade |
| [3], [2, [2], [2, 2], [2, 2, 2, 2]] | 1/3 | 3, 120 | 3, 1 | 3 | cascade |
| [2], [2, [2], [2], [2]], [3, [2], [2], [2]] | 2/3 | 2, 8, 24 | 1, 1, 3 | 3 | cascade |
| [2], [2, 2, 2, 2], [2, 3, 2, 3, 2] | 1/3 | 2, 5, 30 | 1, 1, 3 | 3 | cascade |
| [2], [2, 3, 2, 2, 2, 2, 2, 2, 4] | 1 | 2, 72 | 1, 3 | 3 | cascade |
| [2, 2], [2, 2, 2, 2, 2], [2, 3, 4] | 1 | 3, 6, 18 | 1, 1, 3 | 3 | cascade |
| [2, 2, 2], [2, 3, 2, 2, 2, 3, 2] | 1/3 | 4, 48 | 1, 3 | 3 | cascade |
| [2, 2, 2], [4, 2, 2, 2, 2, 2, 4] | 5/3 | 4, 60 | 1, 3 | 3 | cascade |
| [2, 2, 2, 2], [2, 2, 2, 2], [4, 4] | 5/3 | 5, 5, 15 | 1, 1, 3 | 3 | cascade |
| [2, 2, 2, 2], [2, 3, 2, 2, 2, 4] | 1 | 5, 45 | 1, 3 | 3 | cascade |
| [2, 2, 2, 2, 2, 2], [2, 3, 3, 2] | 1/3 | 7, 21 | 1, 3 | 3 | cascade |
| [2, 3, 2, 2, 2, 2, 2, 2, 3, 2] | 1/3 | 75 | 3 | 3 | cascade |
| [2, 5], [2, 2, 2, 2, 2, 2, 2, 2] | 1 | 9, 9 | 3, 1 | 3 | cascade |
| [3], [6], [2, 2, 2, 2, 2, 2, 2, 2] | 2 | 3, 6, 9 | 3, 3, 1 | 3 | cascade |
| [6], [2, 2, 2, 2, 2, 2, 2, 2, 2] | 5/3 | 6, 10 | 3, 1 | 3 | cascade |
| [2], [2], [2, 4, 2], [2, [2], [2], [2, 2]] | 1/3 | 2, 2, 12, 12 | 1, 1, 3, 1 | 3 | cascade |
| [2], [2], [2, [2], [2], [2, 2, 2, 2, 4]] | 1/3 | 2, 2, 192 | 1, 1, 3 | 3 | cascade |
| [2, 2, 2], [2, 4, 2], [2, [2], [2], [2]] | 1/3 | 4, 12, 8 | 1, 3, 1 | 3 | cascade |
| [2, 2, 2], [2, [2], [2], [2, 2, 2, 4]] | 1/3 | 4, 156 | 1, 3 | 3 | cascade |
| [2, 4, 2], [2, [2], [2], [2, 2, 2, 2]] | 1/3 | 12, 20 | 3, 1 | 3 | cascade |
| [2, [2], [2], [2, 2, 2, 2, 2, 2, 4]] | 1/3 | 264 | 3 | 3 | cascade |
| [3], [2, 2, 2, 2, 2], [2, [2], [2], [4]] | 2/3 | 3, 6, 48 | 3, 1, 3 | 3 | cascade |
| [2, 2], [3, [2], [2], [2]], [3, [2], [2], [2]] | 1/3 | 3, 24, 24 | 1, 3, 3 | 3 | cascade |
| [2, [2], [2], [2]], [2, [2], [2], [2, 2, 4]] | 1/3 | 8, 120 | 1, 3 | 3 | cascade |
| [2, [2], [2], [2, 2]], [2, [2], [2], [2, 4]] | 1/3 | 12, 84 | 1, 3 | 3 | cascade |
| [2, [2], [2], [4]], [2, [2], [2], [2, 2, 2]] | 1/3 | 48, 16 | 3, 1 | 3 | cascade |
| [2], [2, 2, 2, 2, 2, 2, 2], [4, 2, 4] | 2/3 | 2, 8, 24 | 1, 1, 3 | 3 | cascade |
| [2, 2, 2, 2, 2], [2, 4, 2], [2, 4, 2] | 2/3 | 6, 12, 12 | 1, 3, 3 | 3 | cascade |
| [2, 2, 2, 2, 2, 2], [4, 2, 2, 2, 4] | 2/3 | 7, 42 | 1, 3 | 3 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4] | 2/3 | 10, 15 | 1, 3 | 3 | cascade |
| [4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4] | 2/3 | 96 | 3 | 3 | cascade |
| [2], [2], [6], [2, [2], [2], [2, 2, 2, 2, 2]] | 2/3 | 2, 2, 6, 24 | 1, 1, 3, 1 | 3 | cascade |
| [2, 2, 2], [6], [2, [2], [2], [2, 2, 2, 2]] | 2/3 | 4, 6, 20 | 1, 3, 1 | 3 | cascade |
| [6], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2]] | 2/3 | 6, 32 | 3, 1 | 3 | cascade |
| [6], [2, [2], [2], [2]], [2, [2], [2], [2, 2, 2]] | 2/3 | 6, 8, 16 | 3, 1, 1 | 3 | cascade |
| [6], [2, [2], [2], [2, 2]], [2, [2], [2], [2, 2]] | 2/3 | 6, 12, 12 | 3, 1, 1 | 3 | cascade |
| [2, 5], [2, 5], [2, 2, 2, 2, 2, 2, 2, 2] | 1 | 9, 9, 9 | 3, 3, 1 | 3 | cascade |
| [6], [6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 4/3 | 6, 6, 12 | 3, 3, 1 | 3 | cascade |