A normal projective non-Gorenstein log-terminal surface $S$ is called a log del Pezzo surface of index three if the three-times of the anti-canonical divisor $-3K_S$ is an ample Cartier divisor. We classify all log del Pezzo surfaces of index three. The technique for the classification is based on the argument of Nakayama.
Kento FUJITA. Kazunori YASUTAKE. "Classification of log del Pezzo surfaces of index three." J. Math. Soc. Japan 69 (1) 163 - 225, January, 2017. https://doi.org/10.2969/jmsj/06910163