45 singularity types
| Singularity types | \(K^2\) | Orders of local fundamental groups |
Local indices | Index | Cascade |
|---|---|---|---|---|---|
| [7] | 81/7 | 7 | 7 | 7 | cascade |
| [14] | 128/7 | 14 | 7 | 7 | cascade |
| [2], [2, 4] | 50/7 | 2, 7 | 1, 7 | 7 | cascade |
| [2], [2, 11] | 96/7 | 2, 21 | 1, 7 | 7 | cascade |
| [2, 2], [3, 5] | 54/7 | 3, 14 | 1, 7 | 7 | cascade |
| [2], [2], [2, 8, 2] | 64/7 | 2, 2, 28 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2], [2, 4] | 36/7 | 4, 7 | 1, 7 | 7 | cascade |
| [2, 2, 2], [4, 9] | 80/7 | 4, 35 | 1, 7 | 7 | cascade |
| [2], [2, 2], [2, 2, 3] | 24/7 | 2, 3, 7 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2, 2], [3, 5] | 40/7 | 5, 14 | 1, 7 | 7 | cascade |
| [2], [2, 2, 2], [2, 6, 4] | 48/7 | 2, 4, 42 | 1, 1, 7 | 7 | cascade |
| [2, 2], [2, 2], [3, 3, 3] | 27/7 | 3, 3, 21 | 1, 1, 7 | 7 | cascade |
| [2, 2], [2, 2, 2, 2], [2, 4] | 15/7 | 3, 5, 7 | 1, 1, 7 | 7 | cascade |
| [7], [2, 2, 2, 2, 2, 2, 2] | 32/7 | 7, 8 | 7, 1 | 7 | cascade |
| [2, 2, 2], [2, 2, 2], [4, 4, 4] | 32/7 | 4, 4, 56 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2, 2, 2, 2, 2], [8, 8] | 72/7 | 8, 63 | 1, 7 | 7 | cascade |
| [2, 2, 3], [2, 2, 3], [2, 2, 3] | 9/7 | 7, 7, 7 | 7, 7, 7 | 7 | cascade |
| [2], [7], [2, 2, 2, 2, 2, 2, 2, 2] | 18/7 | 2, 7, 9 | 1, 7, 1 | 7 | cascade |
| [2, 2, 2], [2, 2, 2, 2, 2], [3, 5] | 12/7 | 4, 6, 14 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2], [4, 9] | 45/7 | 9, 35 | 1, 7 | 7 | cascade |
| [2, 4], [2, 2, 3], [2, 2, 2, 3, 2] | 8/7 | 7, 7, 14 | 7, 7, 7 | 7 | cascade |
| [2, 4], [2, 4], [2, 2, 2, 2, 2, 2] | 9/7 | 7, 7, 7 | 7, 7, 1 | 7 | cascade |
| [2], [2, 2, 2, 2, 2, 2, 2], [2, 5, 8] | 40/7 | 2, 8, 70 | 1, 1, 7 | 7 | cascade |
| [2, 2, 3], [2, 2, 2, 2, 2, 2], [3, 5] | 8/7 | 7, 7, 14 | 7, 1, 7 | 7 | cascade |
| [2, 2, 3], [2, 2, 2, 3, 2], [3, 3, 3] | 6/7 | 7, 14, 21 | 7, 7, 7 | 7 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 11] | 33/7 | 11, 21 | 1, 7 | 7 | cascade |
| [2, 4], [2, 2, 2, 3, 2], [2, 2, 2, 2, 5] | 6/7 | 7, 14, 21 | 7, 7, 7 | 7 | cascade |
| [2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 10] | 20/7 | 2, 10, 28 | 1, 1, 7 | 7 | cascade |
| [2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 9] | 18/7 | 3, 9, 42 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [4, 3, 8] | 24/7 | 4, 8, 84 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2, 2, 2, 2], [3, 5], [2, 2, 2, 2, 5] | 6/7 | 7, 14, 21 | 1, 7, 7 | 7 | cascade |
| [3, 5], [2, 2, 2, 3, 2], [2, 2, 2, 2, 3, 3] | 4/7 | 14, 14, 28 | 7, 7, 7 | 7 | cascade |
| [2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 11] | 12/7 | 3, 12, 21 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 9] | 10/7 | 5, 10, 35 | 1, 1, 7 | 7 | cascade |
| [2, 2, 2, 2, 5], [2, 2, 2, 2, 5], [2, 2, 2, 2, 5] | 3/7 | 21, 21, 21 | 7, 7, 7 | 7 | cascade |
| [7], [7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 8/7 | 7, 7, 14 | 7, 7, 1 | 7 | cascade |
| [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30/7 | 14, 15 | 7, 1 | 7 | cascade |
| [2], [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16/7 | 2, 14, 16 | 1, 7, 1 | 7 | cascade |
| [2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [8, 2, 8] | 16/7 | 8, 8, 112 | 1, 1, 7 | 7 | cascade |
| [2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 11] | 6/7 | 7, 14, 21 | 7, 1, 7 | 7 | cascade |
| [2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [8, 8] | 9/7 | 9, 9, 63 | 1, 1, 7 | 7 | cascade |
| [3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 10] | 4/7 | 14, 14, 28 | 7, 1, 7 | 7 | cascade |
| [7], [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 6/7 | 7, 14, 21 | 7, 7, 1 | 7 | cascade |
| [2, 11], [2, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 3/7 | 21, 21, 21 | 7, 7, 1 | 7 | cascade |
| [14], [14], [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] | 4/7 | 14, 14, 28 | 7, 7, 1 | 7 | cascade |