Gorenstein Fano threefolds of Picard number one with a $\mathbb{K}^*$-action and maximal orbit quotient $\mathbb{P}_2$

Abstract: We classify the non-toric, $\mathbb{Q}$-factorial, Gorenstein, Fano threefolds of Picard number one with an effective $\mathbb{K}^*$-action and maximal orbit quotient $\mathbb{P}_2$.