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

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