List of toric log del Pezzo surfaces of Picard number one with index 3

18 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, 2], [4, 4] 20/3 4, 15 1, 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], [2, 2, 2], [2, 3, 4] 4 2, 4, 18 1, 1, 3 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], [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], [4, 2, 4] 8/3 4, 4, 24 1, 1, 3 3 cascade
[2, 2, 2, 2], [2, 2, 2, 2], [4, 4] 5/3 5, 5, 15 1, 1, 3 3 cascade
[3], [6], [2, 2, 2, 2, 2, 2, 2, 2] 2 3, 6, 9 3, 3, 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