Summary: We achieve a detailed understanding of the \(n\)-sided planar Poisson-Voronoi cell in the limit of large \(n\). Let \(p_{n}\) be the probability for a cell to have \(n\) sides. We construct the asymptotic expansion of \(\log p_{n}\) up to terms that vanish as \(n \rightarrow \infty\). We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to leading order as \(n \rightarrow \infty\), and after appropriate scaling, these become independent random variables whose laws we determine; and to next order in \(1/{n}\) they have nontrivial long range correlations whose expressions we provide. The \(n\)-sided cell tends towards a circle of radius \((n/4\pi \lambda)^{1/2}\), where \({\lambda}\) is the cell density; hence Lewis’s law for the average area \(A_{n}\) of the \(n\)-sided cell behaves as \(A_{n} \simeq {cn}/\lambda\) with \(c = 1/4\). For \(n \rightarrow \infty\) the cell perimeter, expressed as a function \(R(\phi)\) of the polar angle \(\phi\), satisfies \(d^2 R/d \phi^2 = F(\phi)\), where \(F\) is the known Gaussian noise; we deduce from it the probability law for the perimeter’s long wavelength deviations from circularity. Many other quantities related to the asymptotic cell shape become accessible to calculation.