Let $(B,\Delta,\mathscr{A})$ be the integral affine manifold with singularities described in Example 3.17 and let

$$(B,\Delta,\mathscr{A})\rightarrow(B,\check{\Delta},\check{\mathscr{A}})$$

be its Legendre transform. Let $X(B_{0},\mathscr{A})\hookrightarrow X$ and $X(B_{0},\check{\mathscr{A}})\hookrightarrow\check{X}$ be the corresponding topological semi-stable compactifications. Then $X$ is homeomorphic to the quintic hypersurface and $\check{X}$ is homeomorphic to its mirror.