We present a new method for estimating the 6D pose of rigid objects with available 3D models from a single RGB input image. The method is applicable to a broad range of objects, including challenging ones with global or partial symmetries. An object is represented by compact surface fragments which allow handling symmetries in a systematic manner. Correspondences between densely sampled pixels and the fragments are predicted using an encoder-decoder network. At each pixel, the network predicts: (i) the probability of each object's presence, (ii) the probability of the fragments given the object's presence, and (iii) the precise 3D location on each fragment. A data-dependent number of corresponding 3D locations is selected per pixel, and poses of possibly multiple object instances are estimated using a robust and efficient variant of the PnP-RANSAC algorithm. In the BOP Challenge 2019, the method outperforms all RGB and most RGB-D and D methods on the T-LESS and LM-O datasets. On the YCB-V dataset, it is superior to all competitors, with a large margin over the second-best RGB method.