The quintic threefold $X\subseteq{\bf P}^{4}$ has a well-behaved $T^{3}$-fibration with semistable fibres $f:X\rightarrow B$. If $\check{f}:\check{X}\rightarrow B$ is the dual fibration given by Theorem 0.1, then $\check{X}$ is diffeomorphic to a specific non-singular minimal model of the mirror quintic.