Automatic methods for reconstructing buildings from airborne LiDAR point clouds focus on producing accurate 3D models in a fast and scalable manner, but they overlook the problem of delivering simple and regularized models to practitioners. As a result, output meshes often suffer from connectivity approximations around corners with either the presence of multiple vertices and tiny facets, or the necessity to break the planarity constraint on roof sections and facade components. We propose a 2D planimetric arrangement-based framework to address this problem. We first regularize, not the 3D planes as commonly done in the literature, but a 2D polyhedral partition constructed from the planes. Second, we extrude this partition to 3D by an optimization process that guarantees the planarity of the roof sections as well as the preservation of the vertical discontinuities and horizontal rooftop edges. We show the benefits of our approach against existing methods by producing simpler 3D models while offering a similar fidelity and efficiency.