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Department for Geometry, Faculty of Mathematics, TU Dresden , Dresden , Germany
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Laboratoire GSA, ENSA Paris-Malaquais, Universit´e PSL , Paris , France
Department for Geometry, Faculty of Mathematics, TU Dresden , Dresden , Germany
Koenigs meshes should be more explored in the field of architectural design due to their various fabrication efficiency factors for doubly curved grid-shells. Beside being planar quad meshes (PQ-meshes) they have additional property of duality and are closely linked to graphical statics: their diagonals and those of their dual mesh represent form and force diagrams in equilibrium under a normal unit load. These meshes also fulfill essential geometric criteria such as planar panels suitable for glass cladding. Special subclasses—like discrete isothermic surfaces and discrete minimal surfaces—offer additional advantages, including quad blocks with planar lateral sides (zero geometric torsion) and constant edge offsets. The latter allows for simplified fabrication using straight, discrete strips. Koenigs meshes remain underutilized in architectural practice. This research develops design morphology techniques and parametric tools that preserve their geometric properties, and introduces computational methods for constructing and exploring designs with these networks. The study offers new design strategies of dual meshes and presents practical workflows for implementing Koenigs nets in architectural applications.
discrete Koenigs surfaces, discrete isothermic surfaces, discrete minimal surfaces, architectural geometry, PQ meshes
This contribution is part of the priority program SPP 2187: Adaptive Mod-ular Construction with Flow Production Methods - Precision High-Speed Construc-tion of the Future in the subproject Formwork-free Flow Production of Adaptive Supporting Structures from Variable Frame Elements - Adaptive Concrete Diamond Construction (ACDC) funded by the German Research Foundation (DFG).
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