Formal methods in design have been used for systematic studies in analysis and synthesis of form. The group theoretical approach provides the mathematical language for symmetry, one of the cornerstones of formal composition in architectural design. The recent emphasis of architecture discourse on issues of pattern making and parametric variation only reaffirms the traditional role of symmetry. Still, even if contemporary emphasis on pattern making extends the research in new trajectories, some basic questions regarding the extent of fitness and value of symmetry in formal composition remain unanswered.
This work builds upon recent methodological approaches in the field (March 1998; Park, 2001; Economou, 2003, 2005) and proposes a model that investigates whether the combination of existing group theoretical formalisms with appropriate systems of representation based on 'work on surface' can indeed cast new light in analysis. The object of analysis has been polemically selected here to be the NY5 architecture, a set of designs that are all clearly exemplifying formal qualities of abstraction, layering, complexity, depth and so on, all appearing impenetrable to a systematic and rigorous analysis using the existing group theoretical formal methods.
One specific case study fully illustrates the methodology of analysis, the Smith House by Richard Meier. All plans of the house are represented in three different levels of abstraction moving successively away from the architectural representation to a purely diagrammatic one that foregrounds divisions of space. All representations are fed into an analysis algorithm to pick up all symmetry relationships and the parts are constructed as instances of a binary composition of a family of rectangular grids. Finally the process is reversed to fully account for the construction of the space of the house as a three dimensional layered composition.