List of toric log del Pezzo surfaces of Picard number one with index 6

26 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups		 Local indices Index Cascade
[12] 49/3 12 6 6 cascade
[3, 3], [2, 3, 2, 4] 6 8, 27 2, 3 6 cascade
[2, 5], [3, 2, 2, 2, 3] 5 9, 20 3, 2 6 cascade
[2], [3, 3], [2, 3, 2, 3, 2] 10/3 2, 8, 30 1, 2, 3 6 cascade
[2, 2, 2, 2, 2, 2], [7, 7] 28/3 7, 48 1, 6 6 cascade
[3], [4], [2, 2, 2, 2, 2, 2] 7/3 3, 4, 7 3, 2, 1 6 cascade
[4], [4], [2, 2, 2, 3, 2, 2, 2] 8/3 4, 4, 24 2, 2, 6 6 cascade
[2, 2], [2, 5], [3, 2, 2, 2, 2, 3] 2 3, 9, 24 1, 3, 2 6 cascade
[2, 2, 2], [2, 4, 2], [3, 2, 2, 3] 4/3 4, 12, 16 1, 3, 2 6 cascade
[2, 2, 2], [3, 3], [2, 3, 2, 2, 4] 2 4, 8, 36 1, 2, 3 6 cascade
[3], [2, 5], [2, 2, 2, 3, 2, 2, 2] 2 3, 9, 24 3, 3, 6 6 cascade
[2, 2, 2, 2, 2], [3, 2, 3], [2, 3, 4] 1 6, 12, 18 1, 2, 3 6 cascade
[3, 3], [3, 3], [2, 3, 2, 2, 2, 3, 2] 4/3 8, 8, 48 2, 2, 3 6 cascade
[4], [6], [2, 2, 2, 2, 2, 2, 2, 2, 2] 5/3 4, 6, 10 2, 3, 1 6 cascade
[2, 4, 2], [2, 4, 2], [3, 2, 2, 2, 2, 3] 2/3 12, 12, 24 3, 3, 2 6 cascade
[2, 5], [2, 5], [3, 2, 2, 2, 2, 2, 2, 2, 3] 1 9, 9, 36 3, 3, 2 6 cascade
[4], [2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8] 2 4, 8, 36 2, 1, 6 6 cascade
[12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 13/3 12, 13 6, 1 6 cascade
[2], [12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 7/3 2, 12, 14 1, 6, 1 6 cascade
[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2], [7, 2, 7] 7/3 7, 7, 84 1, 1, 6 6 cascade
[2, 5], [2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8] 1 9, 9, 36 3, 1, 6 6 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [7, 7] 4/3 8, 8, 48 1, 1, 6 6 cascade
[3], [12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 5/3 3, 12, 15 3, 6, 1 6 cascade
[4], [12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 4/3 4, 12, 16 2, 6, 1 6 cascade
[6], [12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 1 6, 12, 18 3, 6, 1 6 cascade
[12], [12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 2/3 12, 12, 24 6, 6, 1 6 cascade