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In this study, we propose a novel high capacity double layer algorithm for secure data embedding in 3D objects. This is achieved by aggregating a cryptography layer through the deployment of Blowfish or AES-128 algorithms to a steganography layer based on a Gray code sequence that individuates the order of the vertices over which the embedding will occur. Thereafter, the 3D objects are preprocessed and the secret data is embedded over the vertices' x-, y- and z- coordinates. Hence, the 3D object capacity is effectively utilized. The secret data is then blindly extracted from the stego 3D object. The performance of the proposed algorithm is extensively investigated and compared to other commensurate studies from the literature. The proposed algorithm withstands vertex reordering and common geometrical similarity attacks such as reflection, uniform scaling, rotation and translation. Additionally, it partially withstands smoothing. The achieved numerical results demonstrate the superiority of the proposed algorithm in terms of capacity, computational complexity, imperceptibility, distortion and robustness.