Geodesic
Combining globally rigid frameworks
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 202-209

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It is shown how to combine two generically globally rigid bar frameworks in $d$-space to get another generically globally rigid framework. The construction is to identify $d+1$ vertices from each of the frameworks and erase one of the edges that they have in common. 
@article{TM_2011_275_a12,
     author = {R. Connelly},
     title = {Combining globally rigid frameworks},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {202--209},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_275_a12/}
}
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R. Connelly. Combining globally rigid frameworks. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 202-209. http://geodesic.mathdoc.fr/item/TM_2011_275_a12/