List of quotient singularities with index 18

21 basic regular quotient singularity types and 30 irregular quotient singularity types

Singularity type Index
[36] 18
[4, 5, 4] 18
[20, 3, 4] 18
[22, 3, 2] 18
[3, 5, 2, 2] 18
[4, 4, 3, 3] 18
[20, 2, 3, 3] 18
[21, 3, 2, 2] 18
[2, 3, 8, 3, 2] 18
[3, 3, 3, 3, 3] 18
[4, 3, 4, 3, 4] 18
[4, 3, 6, 3, 2] 18
[2, 3, 7, 3, 2, 2] 18
[3, 3, 2, 6, 3, 2] 18
[4, 3, 4, 2, 3, 3] 18
[4, 3, 5, 3, 2, 2] 18
[2, 2, 3, 6, 3, 2, 2] 18
[3, 3, 2, 4, 2, 3, 3] 18
[3, 3, 2, 5, 3, 2, 2] 18
[2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[20, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 3, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[4, 3, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 2, 3, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[3, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
Basic singularity type Second singularity type Third singularity type Index
[19, 19] [19, 2, 19] [19, 2, 2, 19] 18
[19, 3, 3, 4] [19, 2, 3, 3, 4] [19, 2, 2, 3, 3, 4] 18
[19, 5, 3, 2] [19, 2, 5, 3, 2] [19, 2, 2, 5, 3, 2] 18
[19, 3, 2, 3, 3] [19, 2, 3, 2, 3, 3] [19, 2, 2, 3, 2, 3, 3] 18
[19, 4, 3, 2, 2] [19, 2, 4, 3, 2, 2] [19, 2, 2, 4, 3, 2, 2] 18
[2, 3, 5, 5, 3, 2] [2, 3, 5, 2, 5, 3, 2] [2, 3, 5, 2, 2, 5, 3, 2] 18
[4, 3, 3, 3, 3, 4] [4, 3, 3, 2, 3, 3, 4] [4, 3, 3, 2, 2, 3, 3, 4] 18
[4, 3, 3, 5, 3, 2] [4, 3, 3, 2, 5, 3, 2] [4, 3, 3, 2, 2, 5, 3, 2] 18
[2, 3, 5, 4, 3, 2, 2] [2, 3, 5, 2, 4, 3, 2, 2] [2, 3, 5, 2, 2, 4, 3, 2, 2] 18
[3, 3, 2, 3, 5, 3, 2] [3, 3, 2, 3, 2, 5, 3, 2] [3, 3, 2, 3, 2, 2, 5, 3, 2] 18
[4, 3, 3, 3, 2, 3, 3] [4, 3, 3, 2, 3, 2, 3, 3] [4, 3, 3, 2, 2, 3, 2, 3, 3] 18
[4, 3, 3, 4, 3, 2, 2] [4, 3, 3, 2, 4, 3, 2, 2] [4, 3, 3, 2, 2, 4, 3, 2, 2] 18
[2, 2, 3, 4, 4, 3, 2, 2] [2, 2, 3, 4, 2, 4, 3, 2, 2] [2, 2, 3, 4, 2, 2, 4, 3, 2, 2] 18
[3, 3, 2, 3, 3, 2, 3, 3] [3, 3, 2, 3, 2, 3, 2, 3, 3] [3, 3, 2, 3, 2, 2, 3, 2, 3, 3] 18
[3, 3, 2, 3, 4, 3, 2, 2] [3, 3, 2, 3, 2, 4, 3, 2, 2] [3, 3, 2, 3, 2, 2, 4, 3, 2, 2] 18
[19, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [19, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [19, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 3, 5, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [2, 3, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [2, 3, 5, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [4, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [4, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 2, 3, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [2, 2, 3, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [2, 2, 3, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] [3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 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, 2, 3, 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, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 18

Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87