We finally have a way to calculate if a 3D building will stand up even if it doesn't have a single flat surface on it.
arXiv · March 13, 2026 · 2603.12093
Why it matters
Traditional engineering usually requires the gaps in a building's frame to be flat to ensure the structure won't collapse. By applying 'homology theory' from abstract mathematics, researchers have found a way to guarantee the stability of twisted, curvy frames that were previously thought impossible to model accurately.
From the abstract
This paper extends graphic statics by describing the forces and moments in any 3D rigid-jointed frame structure in terms of cell complexes using homology theory of algebraic topology. Graphic statics provides a highly geometric way to represent the equilibrium in bar structures. Unlike traditional matrix-based linear structural analysis which represents a structure as a set of nodes connected by bars, graphic statics imagines that the bar network defines a variety of higher-dimensional objects (