  We show how to deform the map $\operatorname{Log}\colon (\mathbb{C}^*)^n \to
\mathbb{R}^n$ such that the image of the complex pair of pants $P^\circ \subset
{(\mathbb{C}^*)^n}$ is the tropical hyperplane by showing an (ambient) isotopy
between $P^\circ \subset {(\mathbb{C}^*)^n}$ and a natural polyhedral
subcomplex of the product of the two skeleta $S\times \Sigma \subset
\mathcal{A} \times \mathcal{C}$ of the amoeba $\mathcal{A}$ and the coamoeba
$\mathcal{C}$ of $P^\circ$. This lays the groundwork for having the
discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus
fibrations.
