We present a deep learning method for end-to-end monocular 3D object detection and metric shape retrieval. We propose a novel loss formulation by lifting 2D detection, orientation, and scale estimation into 3D space. Instead of optimizing these quantities separately, the 3D instantiation allows to properly measure the metric misalignment of boxes. We experimentally show that our 10D lifting of sparse 2D Regions of Interests (RoIs) achieves great results both for 6D pose and recovery of the textured metric geometry of instances. This further enables 3D synthetic data augmentation via inpainting recovered meshes directly onto the 2D scenes. We evaluate on KITTI3D against other strong monocular methods and demonstrate that our approach doubles the AP on the 3D pose metrics on the official test set, defining the new state of the art.