Geometry lies at the core of the architectural design process. It is ever present, from the very first attempts of form-finding to the final stages of construction. The modern tools of geometric computing for efficient design, analysis, and manufacturing of complex shapes open up new perspectives for architecture. Architecture, in turn, poses new problems to geometry. It is precisely around these topics, at the common border of geometry processing and architectural design, where the new research area of architectural geometry is situated. Advances in Architectural Geometry is the premier venue for disseminating new research ideas and cutting-edge results at the interface of geometry processing and architectural design. AAG12 brings together researchers from all related areas and takes place in Paris in September 2012.