  As a standard example in toric geometry, the Atiyah flop of a $(-1,-1)$-curve
in a smooth 3-fold can be described combinatorially in terms of the two
possible triangulations of a square cone. The flop of $(-2,0)$-curve cannot be
realised in terms of toric geometry. Nevertheless, we explain how to construct
a cone $\sigma$ in an integral affine manifold with singularities associated to
the singularity $(P\in Y)$ at the base of a $(-2,0)$-flop. The two sides of the
flop can then be described combinatorially in terms of two different
subdivisions of $\sigma$. As an interesting byproduct of our construction, we
can build a singularity $(P^\star\in Y^\star)$ which is mirror to $(P\in Y)$.
