Data.

To enhance the robustness of single 3D model carriers in information hiding, this paper proposes a multi-carrier steganography algorithm based on vertex projection of 3D models. The algorithm improves the embedding capacity and attack resistance by fusing multiple 3D models into a geometrically invariant space using centroid coincidence and tangent plane projection. Secret information is embedded by adjusting the position of central vertices in the projection plane of their 1-ring neighborhoods. Experimental results demonstrate that the proposed method achieves strong robustness against translation, rotation, simplification, random noise, and shear attacks. Specifically, the proposed algorithm achieves a peak SNR of 47.87 dB on the xyzrgb_dragon model, significantly outperforming other algorithms, and maintains a lower BER under various attack intensities—for instance, less than 0.1 under 30% simplification and 0.001 random noise. These results confirm the superior invisibility and robustness of the proposed multi-carrier information hiding scheme.