The moduli space of genus 8 Fano 3-folds with two frac12(1,1,1)-points: rationality and K-stability

Let $\mathcal F_{8,2\times\frac12(1,1,1)}$ be the moduli space of genus $8$ Fano $3$-folds with two terminal quotient singularities of type $\frac12(1,1,1)$. We prove that $\mathcal F_{8,2\times\frac12(1,1,1)}$ is rational. Moreover, we show that a general member of this family is K-stable.