  In a previous work, we gave a construction of (not necessarily realizable)
oriented matroids from a triangulation of a product of two simplices. In this
follow-up paper, we use a variant of Viro's patchworking to derive a
topological representation of the oriented matroid directly from the polyhedral
structure of the triangulation, hence finding a combinatorial manifestation of
patchworking besides tropical algebraic geometry. We achieve this by rephrasing
the patchworking procedure as a controlled cell merging process, guided by the
structure of tropical oriented matroids. A key insight is a new promising
technique to show that the final cell complex is regular.
