In this letter, we introduce PolarMesh as a star-convex approximation of a 3D object based on spherical projection and can be applied to monocular object pose and shape estimation. The proposed PolarMesh can be stored in a discrete 2D map that allows a trivial conversion between it and the object surface, as the adjacent map elements form faces of the 3D model. The fixed-grid 2D nature of this object surface approximation ensures that it can be estimated from an image patch of the object with an auto-encoder neural network. Moreover, the PolarMesh not only encodes the object shape but also its orientation. Consequently, it is used for accurate estimation of object orientation and can be extended to the full 6D pose estimation using a projection-based method for translation. An exhaustive quantitative evaluation on LineMod, LineMod-Occlusion and HomebrewedDB shows the competitive performance of the proposed method compared to other monocular RGB pose estimation pipelines. Furthermore, we tested the generalization capabilities of the representation on the recent NOCS dataset for category-level pose estimation and achieved very compelling results in terms of predicted rotations.