We give an example of a simple oriented matroid 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. (C) 1996 Academic Press, Inc. [References: 18]
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