"The essential ingredients of a shell structure... are continuity and curvature. ...[S]hells are structurally continuous in the sense that they can transmit forces in a number of different directions in the surface of the shell... These have a quite different mode of action from skeletal structures... only capable of transmitting forces along discrete structural members. ...There seems to be a principle that closed surfaces are rigid. This principle is used in many areas of engineering construction. ...[A]lthough the ideas of 'closed' and 'open' shells... are fairly clear, it is difficult to quanitify intermediate cases into which... the majority of actual shell structures fall. ...There is a theorem, due to Cauchy, which states that a convex polyhedron is rigid. ...[N]on-convexity may produce deformability. ...While rigidity and strength are in many cases desirable attributes of shell structures, there are some important difficulties which can occur... [involving] unavoidable rigidity. ...[A] second broad principle... may be stated thus: efficient structures may fail catastrophically. Here I use the term 'efficient' to describe the consequences of employing the first principle. By designing a structure as... closed... we may be able to use thinner sheet material, and hence produce an economical, or efficient, design."