Rigidity with few locations

Karim Adiprasito*, Eran Nevo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size of A increases with the genus. The assertion fails, namely no such finite A exists, for the larger family of all graphs that are generically rigid in 3-space and even in the plane.

Original languageAmerican English
Pages (from-to)711-723
Number of pages13
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Oct 2020

Bibliographical note

Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.


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