27 singularity types
| Singularity types | \(K^2\) | Orders of local fundamental groups |
Local indices | Index | Cascade |
|---|---|---|---|---|---|
| [16] | 81/4 | 16 | 8 | 8 | cascade |
| [2, 2], [3, 11] | 27/2 | 3, 32 | 1, 8 | 8 | cascade |
| [2], [2], [2, 5, 2] | 25/4 | 2, 2, 16 | 1, 1, 8 | 8 | cascade |
| [2, 2], [2, 2], [3, 6, 3] | 27/4 | 3, 3, 48 | 1, 1, 8 | 8 | cascade |
| [4], [2, 2, 2], [2, 2, 2, 2, 4] | 9/4 | 4, 4, 16 | 2, 1, 8 | 8 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2], [9, 9] | 45/4 | 9, 80 | 1, 8 | 8 | cascade |
| [2, 2, 2], [2, 5, 2], [3, 2, 2, 2, 3] | 5/4 | 4, 16, 20 | 1, 8, 2 | 8 | cascade |
| [4], [3, 2, 3], [2, 2, 2, 2, 2, 4, 2] | 3/2 | 4, 12, 32 | 2, 2, 8 | 8 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 11] | 11/2 | 11, 32 | 1, 8 | 8 | cascade |
| [2, 3, 2], [2, 5, 2], [3, 2, 2, 2, 2, 3] | 3/4 | 8, 16, 24 | 4, 8, 2 | 8 | cascade |
| [3, 3], [2, 2, 2, 2, 4], [2, 2, 4, 2, 2] | 3/4 | 8, 16, 24 | 2, 8, 4 | 8 | cascade |
| [2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 10] | 15/4 | 2, 10, 48 | 1, 1, 8 | 8 | cascade |
| [2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [3, 4, 9] | 9/2 | 3, 9, 96 | 1, 1, 8 | 8 | cascade |
| [2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4], [5, 5] | 3/4 | 8, 16, 24 | 1, 8, 4 | 8 | cascade |
| [2, 2, 2, 2, 4], [2, 2, 2, 2, 4], [2, 2, 3, 5] | 1/2 | 16, 16, 32 | 8, 8, 4 | 8 | cascade |
| [2, 2, 6], [3, 2, 2, 3], [2, 2, 2, 2, 2, 4, 2] | 1/2 | 16, 16, 32 | 4, 2, 8 | 8 | cascade |
| [2, 5, 2], [2, 5, 2], [3, 2, 2, 2, 2, 2, 2, 3] | 1/2 | 16, 16, 32 | 8, 8, 2 | 8 | cascade |
| [2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 11] | 3/2 | 4, 12, 32 | 1, 1, 8 | 8 | cascade |
| [3, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 10] | 3/4 | 12, 12, 48 | 2, 1, 8 | 8 | cascade |
| [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 17/4 | 16, 17 | 8, 1 | 8 | cascade |
| [2], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 9/4 | 2, 16, 18 | 1, 8, 1 | 8 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [9, 2, 9] | 9/4 | 9, 9, 144 | 1, 1, 8 | 8 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 9] | 5/4 | 10, 10, 80 | 1, 1, 8 | 8 | cascade |
| [2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 11] | 1/2 | 16, 16, 32 | 4, 1, 8 | 8 | cascade |
| [4], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 5/4 | 4, 16, 20 | 2, 8, 1 | 8 | cascade |
| [8], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 3/4 | 8, 16, 24 | 4, 8, 1 | 8 | cascade |
| [16], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 1/2 | 16, 16, 32 | 8, 8, 1 | 8 | cascade |