(eng): In this paper, we introduce new 3D rotation moment invariants, which are composed of non-separable Appell moments. The Appell moments can be substituted directly into the 3D rotation invariants instead of the geometric moments without violating their invariance. We show that non-separable moments may outperform the separable ones in terms of recognition power and robustness thanks to a better distribution of their zero surfaces over the image space. We test the numerical properties and discrimination power of the proposed invariants on three real datasets – MRI images of human brain, 3D scans of statues, and confocal microscope images of worms.