Whether a framework is rigid depends not only on counting constraints and freedoms, but also on the particular geometry of the framework. Some frameworks are flexible despite being over-constrained, but there are also special configurations in even the most pedestrian frameworks that are rigid despite being under-constrained or that show branched configuration spaces. This second set of special cases turn out to be ubiquitous and surprisingly easy to find. In continuum shells, there is also a relationship between self-stresses and isometries - deformations that do not stretch the shell - but this relationship seems even murkier. First, I will exhibit a very general one-to-one correspondence between self-stresses and isometries of a shell that shows - perhaps unsurprisingly - that the boundaries of the shell have a lot to say about the shell’s rigidity. Finally, I will discuss an example of a family of twisted, elastic minimal surfaces where the shell’s topology does control its global rigidity. When a shell has suitable bending prestresses, it can develop a mode that, modulo imperfections, cost no energy to actuate. It turns out that the rigidity depends on the number of half-twists: an odd number is always rigid (because of nonorientability), but zero and two half-twists are also rigid through a completely distinct mechanism. I will not draw any conclusions but I do hope to draw your attention to how the continuum and discrete problems may be related.