Flexing on Topology, or, Contrapposto Architecture

Abstract

In 1977, mathematician Robert Connelly discovered a unique eighteen-sided closed, hinged polyhedron that, remarkably, wiggled, overturning centuries of mathematical discourse linking polyhedra with rigidity. This new category of polyhedra is the source of an ongoing interdisciplinary collaboration between architecture and discrete geometry. The flexible polyhedron serves as a generative design tool to develop a new approach to structure and a new relationship of the body in space, as well as an analytical lens through which to understand and challenge the history of architecture’s close association with upright rigidity. In the late 1960s, the Architecture Principe Group (Paul Virilio and Claude Parent), argued against propriety and restraint with a theory of the body that challenged upright posture. The oblique function replaced a system of rigid proportions of a universal body at rest in Euclidean space with the figure of the dancer put in motion by the forces of gravity on the oblique. However, Virilio laments their non-orthogonal system of continuous folded planes became “all blobs, blobs, blobs.” Taking topological thinking filtered through Deleuze, Greg Lynn and others harnessed emerging computer technology to produce infinite variations of doubly-curved, amorphous spheres. The seamless smoothness of “animate form”, how¬ever, ensured mathematical rigidity, a result of which Lynn is undoubtedly aware as he employs new robotic technologies to re-animate his forms. In this context, flexible polyhedra are both incredibly simple geometric forms in a world of complex-curved topological spheres; and much more complex, capable of flexibility without abandoning geometry or rigidity and without cutting-edge technologies. To borrow a phrase, the flexible polyhedron is both square and groovy. This ongoing interdisciplinary project reveals the false distinction between geometry and topology as interpreted by the architectural discipline, and explores the architectural ramifications of this new world of flexible polyhedra while using material/spatial practice to further understand and represent topology.