Estimating 6D poses of rigid objects from RGB images is an important but challenging task. This is especially true for textureless objects with strong symmetry, since they have only sparse visual features to be leveraged for the task and their symmetry leads to pose ambiguity. The implicit encoding of orientations learned by autoencoders  , has demonstrated its effectiveness in handling such objects without requiring explicit pose labeling. In this letter, we further improve this methodology with two key technical contributions. First, we use edge cues to complement the color images with more discriminative features and reduce the domain gap between the real images for testing and the synthetic ones for training. Second, we enhance the regularity of the implicitly learned pose representations by a self-supervision scheme to enforce the geometric prior that the latent representations of two images presenting nearby rotations should be close too. Our approach achieves the state-of-the-art performance on the T-LESS benchmark in the RGB domain; its evaluation on the LINEMOD dataset also outperforms other synthetically trained approaches. Extensive ablation tests demonstrate the improvements enabled by our technical designs. Our code is publicly available for research use.