  A tensegrity is a structure made from cables, struts and stiff bars. A
$d$-dimensional tensegirty is universally rigid if it is rigid in any dimension
$d'$ with $d'\geq d$. 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 representation
of finite groups.
