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A <jats:italic>d<\/jats:italic>-dimensional tensegrity is universally rigid if it is rigid in any dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$d'$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>\u2032<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:tex-math>$$d'\\ge d$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>d<\/mml:mi>\n                      <mml:mo>\u2032<\/mml:mo>\n                    <\/mml:msup>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mi>d<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The celebrated super stability condition due to Connelly gives a sufficient condition for a tensegrity to be universally rigid. Gortler and Thurston showed that super stability characterizes universal rigidity when the point configuration is generic and every member is a stiff bar. We extend this result in two directions. We first show that a generic universally rigid tensegrity is super stable. We then extend it to tensegrities with point group symmetry, and show that this characterization still holds as long as a tensegrity is generic modulo symmetry. Our strategy is based on the block-diagonalization technique for symmetric semidefinite programming problems, and our proof relies on the theory of real irreducible representations of finite groups.<\/jats:p>","DOI":"10.1007\/s10107-021-01730-2","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T10:02:59Z","timestamp":1638180179000},"page":"109-145","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Characterizing the universal rigidity of generic tensegrities"],"prefix":"10.1007","volume":"197","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0814-8419","authenticated-orcid":false,"given":"Ryoshun","family":"Oba","sequence":"first","affiliation":[]},{"given":"Shin-ichi","family":"Tanigawa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,29]]},"reference":[{"issue":"10","key":"1730_CR1","doi-asserted-by":"publisher","first-page":"1244","DOI":"10.1016\/j.dam.2006.11.011","volume":"155","author":"AY Alfakih","year":"2007","unstructured":"Alfakih, A.Y.: On dimensional rigidity of bar-and-joint frameworks. 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