In 1813 Cauchy proved that strictly convex triangulated spheres in three-space have a unique strictly convex realization, whose proof had an annoying but correctable mistake that involved a more subtle idea of an opening arm. This "arm lemma" really involves a concept of "universal rigidity" for a tensegrity with non-extendable chains and non-contractable struts, where the object, a tensegrity, has a unique realization, universal rigidity, satisfying the cable and strut conditions in all higher Euclidean dimensions. This in turn comes from the concept of a "stress matrix" whose rank alone determines "generic" global rigidity in a fixed Euclidean dimension for bar frameworks. This is fine, but the generic condition is an annoying mystery. Here we look at collections of tensegrities, where universal rigidity, and even global rigidity, can be determined sometimes positively, sometimes negatively, and sometimes we don't know. One collection of recent examples is when the vertices are in strictly convex position in the plane, where convex rigidity as related to infinitesimal rigidity is generalized from dimension three to dimension two. Another example is when a three-rung ladder is in the line, which gives a very complete answer to a nice question about universal rigidity of frameworks of Tibor Jordan. I will have numerous examples where people can touch and feel the rigidity sensually. This is joint work with Bryan Chen, Tony Nixon, Shlomo Gortler, Louis Theran, Bill Jackson, Shin-ichi Tanagawa, and Albert Zhang.