A pseudoconfiguration of points without adjoint (Q1125955)

We give an example of a simple oriented matroid \(\mathcal D\) that admits an oriented adjoint. Furthermore, any adjoint of the underlying matroid \(D\), does not itself admit an adjoint. \(D\) arises from the well-known non-Desargues matroid by a coextension by a coparallel element and, hence, has rank 4. The orientability of \(D\) and some of its adjoints follows from an apparently new oriented matroid construction given in the paper that is a very special case of an amalgam of two copies of one oriented matroid.