List of quotient singularities with index 1

2 basic regular quotient singularity types and 4 irregular quotient singularity types

Singularity type Index
[2] 1
[2, [2], [2, 2], [2, 2]] 1
[2, [2], [2, 2], [2, 2, 2]] 1
[2, [2], [2, 2], [2, 2, 2, 2]] 1
Basic singularity type Second singularity type Third singularity type Index
[2, 2] [2, 2, 2] [2, 2, 2, 2] 1
[2, [2], [2], [2]] [2, [2], [2], [2, 2]] [2, [2], [2], [2, 2, 2]] 1

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