A collapsing ancient solution of mean curvature flow in ${\mathbb{R}}^3$

We construct a compact, convex ancient solution of mean curvature flow in ${\mathbb{R}}^{n+1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $\pi$ and in no smaller slab.