Concepts from isotropic geometry, Timoshenko’s shell theory, Airy stress functions and Maxwell’s reciprocal diagrams are combined in the design of plane-faced funicular gridshells. The notions of self-Airy and mixed-Airy gridshells are introduced, with an emphasis on self-tied gridshells. This paper extends the work of J.C. Maxwell for 2D pin-jointed trusses to 2.5D gridshells with the addition of a new reciprocal figure called the slope diagram. The form, force and slope diagrams are combined by a mixed area calculation to produce another new figure called the Maxwell-Mondrian diagram. A powerful new design process leveraging the relationship between the gridshell geometry and the Airy stress function is presented.