Vertex Splitting, Coincident Realisations, and Global Rigidity of Braced Triangulations

We give a relatively short graph theoretic proof of a result of Jordán and Tanigawa that a 4-connected graph which has a spanning plane triangulation as a proper subgraph is generically globally rigid in ℝ^3 . Our proof is based on a new sufficient condition for the so called vertex splitting operation to preserve generic global rigidity in ℝ^d .