  We analyse the local structure of the K-moduli space of Fano varieties at a
toric singular K-polystable Fano 3-fold, which deforms to smooth Fano 3-folds
with anticanonical volume 28 and Picard rank 4. In particular, by constructing
an algebraic deformation of this toric singular Fano, we show that the
irreducible component of K-moduli parametrising these smooth Fano 3-folds is a
rational surface.
