List of toric log del Pezzo surfaces of Picard number one with index 12

53 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups		 Local indices Index Cascade
[24] 169/6 24 12 12 cascade
[3], [2, 2, 6] 25/3 3, 16 3, 4 12 cascade
[2], [2], [2, 7, 2] 49/6 2, 2, 24 1, 1, 12 12 cascade
[3], [3], [2, 2, 4, 2, 2] 25/6 3, 3, 24 3, 3, 4 12 cascade
[4, 4], [2, 2, 3, 2, 2, 5] 20/3 15, 64 3, 4 12 cascade
[2, 2, 6], [4, 2, 2, 2, 2, 4] 17/3 16, 51 4, 3 12 cascade
[3], [2, 2, 2, 2], [2, 2, 3, 5] 10/3 3, 5, 32 3, 1, 4 12 cascade
[2], [2, 3, 4], [2, 2, 3, 3, 2, 2] 5/2 2, 18, 40 1, 3, 4 12 cascade
[2], [2, 2, 6], [2, 3, 2, 2, 2, 2, 4] 3 2, 16, 54 1, 4, 3 12 cascade
[2, 2], [2, 2, 4, 2, 2], [2, 3, 2, 4] 3/2 3, 24, 27 1, 4, 3 12 cascade
[2, 3, 2], [2, 4, 2], [3, 2, 2, 2, 3] 5/6 8, 12, 20 4, 3, 2 12 cascade
[3], [4, 4], [2, 2, 3, 2, 2, 3, 2, 2] 5/2 3, 15, 72 3, 3, 4 12 cascade
[3], [8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 11/6 3, 8, 11 3, 4, 1 12 cascade
[2, 2, 2], [2, 2, 6], [4, 2, 2, 2, 2, 2, 4] 5/3 4, 16, 60 1, 4, 3 12 cascade
[2, 2, 2], [2, 7, 2], [3, 2, 2, 2, 2, 2, 3] 7/6 4, 24, 28 1, 12, 2 12 cascade
[2, 2, 2, 2], [4, 4], [2, 2, 3, 2, 2, 2, 5] 5/3 5, 15, 80 1, 3, 4 12 cascade
[2, 2, 2, 2, 2], [2, 3, 4], [2, 2, 3, 2, 5] 1 6, 18, 48 1, 3, 4 12 cascade
[3, 2, 3], [2, 2, 4, 2, 2], [2, 3, 2, 2, 4] 1/2 12, 24, 36 2, 4, 3 12 cascade
[3, 3], [2, 2, 2, 3, 2, 2, 2], [2, 2, 3, 5] 2/3 8, 24, 32 2, 6, 4 12 cascade
[4], [2, 2, 6], [2, 2, 2, 2, 4, 2, 2, 2, 2] 5/3 4, 16, 60 2, 4, 6 12 cascade
[2, 2, 2, 2, 2, 2, 2], [4, 2, 4], [2, 2, 3, 5] 2/3 8, 24, 32 1, 3, 4 12 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [13, 13] 91/6 13, 168 1, 12 12 cascade
[2, 3, 2], [2, 7, 2], [3, 2, 2, 2, 2, 2, 2, 3] 2/3 8, 24, 32 4, 12, 2 12 cascade
[2, 3, 4], [2, 3, 4], [2, 2, 3, 2, 2, 3, 2, 2] 1/2 18, 18, 72 3, 3, 4 12 cascade
[3, 3], [2, 2, 6], [2, 3, 2, 2, 2, 2, 2, 2, 4] 1 8, 16, 72 2, 4, 3 12 cascade
[6], [2, 3, 4], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3] 1 6, 18, 48 3, 3, 12 12 cascade
[8], [2, 3, 2], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3] 4/3 8, 8, 48 4, 4, 12 12 cascade
[2, 4, 2], [2, 7, 2], [3, 2, 2, 2, 2, 2, 2, 2, 3] 1/2 12, 24, 36 3, 12, 2 12 cascade
[4, 2, 4], [2, 2, 2, 3, 2, 2, 2], [2, 2, 3, 2, 5] 1/3 24, 24, 48 3, 6, 4 12 cascade
[4, 4], [4, 4], [2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2] 5/6 15, 15, 120 3, 3, 4 12 cascade
[6], [8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 7/6 6, 8, 14 3, 4, 1 12 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 6], [2, 2, 2, 2, 3, 7] 1 8, 16, 72 1, 4, 6 12 cascade
[2, 2, 6], [2, 2, 6], [2, 2, 2, 2, 3, 3, 2, 2, 2, 2] 2/3 16, 16, 96 4, 4, 6 12 cascade
[8], [3, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2] 1 8, 16, 72 4, 2, 12 12 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 4, 14] 14/3 2, 14, 96 1, 1, 12 12 cascade
[2, 2, 6], [2, 2, 6], [4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4] 2/3 16, 16, 96 4, 4, 3 12 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 5], [2, 2, 2, 2, 8] 1/2 12, 24, 36 1, 4, 6 12 cascade
[2, 7, 2], [2, 7, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 1/3 24, 24, 48 12, 12, 2 12 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 15] 5/2 3, 15, 72 1, 1, 12 12 cascade
[2, 3, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 15] 1 8, 16, 72 4, 1, 12 12 cascade
[8], [12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 5/6 8, 12, 20 4, 6, 1 12 cascade
[3, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 4, 14] 2/3 16, 16, 96 2, 1, 12 12 cascade
[2, 3, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 15] 1/2 18, 18, 72 3, 1, 12 12 cascade
[24], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 25/6 24, 25 12, 1 12 cascade
[2], [24], [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] 13/6 2, 24, 26 1, 12, 1 12 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [13, 2, 13] 13/6 13, 13, 312 1, 1, 12 12 cascade
[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], [13, 13] 7/6 14, 14, 168 1, 1, 12 12 cascade
[3], [24], [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] 3/2 3, 24, 27 3, 12, 1 12 cascade
[4], [24], [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] 7/6 4, 24, 28 2, 12, 1 12 cascade
[6], [24], [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] 5/6 6, 24, 30 3, 12, 1 12 cascade
[8], [24], [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] 2/3 8, 24, 32 4, 12, 1 12 cascade
[12], [24], [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, 2, 2, 2, 2] 1/2 12, 24, 36 6, 12, 1 12 cascade
[24], [24], [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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 1/3 24, 24, 48 12, 12, 1 12 cascade