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Graph."],"published-print":{"date-parts":[[2017,12,31]]},"abstract":"<jats:p>Three-dimensional structures in building construction and architecture are realized with conflicting goals in mind: engineering considerations and financial constraints easily are at odds with creative aims. It would therefore be very beneficial if optimization and side conditions involving statics and geometry could play a role already in early stages of design, and could be incorporated in design tools in an unobtrusive and interactive way. This paper, which is concerned with a prominent class of structures, is a substantial step towards this goal. We combine the classical work of Maxwell, Michell, and Airy with differential-geometric considerations and obtain a geometric understanding of \"optimality\" of surface-like lightweight structures. It turns out that total absolute curvature plays an important role. 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