The design of structural "spider webs"

Dedicated to Prof. Werner Sobek on the occasion of his 65th birthday
In 1864, James Clerk Maxwell wrote the remarkable paper “On Reciprocal Figures and Diagrams of Forces.” Maxwell observed that for a frame (what today would be called a truss or a net) to be in equilibrium, it must be the projection of a plane-faced polyhedron. It is now known that this observation is correct, provided the bars of the truss or net and the lines of the external applied forces can be represented by a planar graph. We also know that the plane-faced polyhedron is the Airy stress function.
This information can greatly assist a structural designer in creating, adjusting, and analysing structural nets. These nets can be planar structures or the planar projections of three dimensional nets (including spider webs). Simple visual techniques can be used to evaluate how many independent states of self-stress exist and how to adjust the design to achieve goals such as targeted geometries, redundancies or forces. Combined with force-density form finding, this process creates a powerful design tool. This paper will review the theoretical background and applications of the design process.