  We introduce dual matroids of 2-dimensional simplicial complexes. Under
certain necessary conditions, duals matroids are used to characterise
embeddability in 3-space in a way analogous to Whitney's planarity criterion.
  We further use dual matroids to extend a 3-dimensional analogue of
Kuratowski's theorem to the class of 2-dimensional simplicial complexes
obtained from simply connected ones by identifying vertices or edges.
