The asymptotic metric-dimension conjecture for maximal planar graphs

Let $G$ be a maximal planar graph with $n$ vertices, and let $\beta$ denote its metric dimension. The asymptotic metric-dimension conjecture. For maximal planar graphs,

$$\beta = \floor{\frac{2n}{5}} + O(1).$$

The conjecture is motivated by small cases and by the metric dimension of bipyramids; determining matching bounds for all maximal planar graphs remains open.