List of toric log del Pezzo surfaces of Picard number one with index 4

13 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], [5, 5] 15/2 5, 24 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, 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, 3, 2], [2, 3, 2], [3, 2, 2, 3] 1 8, 8, 16 4, 4, 2 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, 2], [2, 2, 2, 2], [5, 2, 5] 5/2 5, 5, 40 1, 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
[4], [8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 3/2 4, 8, 12 2, 4, 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