All \(11_ 3\) and \(12_ 3\)-configurations are rational (Q923089)

An \(n_ 3\)-configuration consists of n points and n lines such that each point and line is incident with exactly three lines and points, respectively. The following conjecture is due to B. Grünbaum: Every \(n_ 3\)-configuration which can be realized in PG(2,\({\mathbb{R}})\) is also realizable in PG(2,\({\mathbb{Q}})\). By \textit{J. Bokowski} and the first author [Computational synthetic geometry (1989; Zbl 0683.05015)] this is true for \(n\leq 10\). The authors extend this result to \(n=11\) and \(n=12\).