Abstract: Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes-those having planar faces-are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least-squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints.