  Every tropical ideal in the sense of Maclagan-Rinc\'on has an associated
tropical variety, a finite polyhedral complex equipped with positive integral
weights on its maximal cells. This leads to the realisability question,
ubiquitous in tropical geometry, of which weighted polyhedral complexes arise
in this manner. Using work of Las Vergnas on the non-existence of tensor
products of matroids, we prove that there is no tropical ideal whose variety is
the Bergman fan of the direct sum of the V\'amos matroid and the uniform
matroid of rank two on three elements, and in which all maximal cones have
weight one.
