This paper presents a hierarchical watermarking framework for semiregular meshes. Three blind watermarks are inserted in a semiregular mesh with different purposes: a geometrically robust watermark for copyright protection, a high-capacity watermark for carrying a large amount of auxiliary information, and a fragile watermark for content authentication. The proposed framework is based on wavelet transform of the semiregular mesh. More precisely, the three watermarks are inserted in different appropriate resolution levels obtained by wavelet decomposition of the mesh: the robust watermark is inserted by modifying the norms of the wavelet coefficient vectors associated with the lowest resolution level; the fragile watermark is embedded in the high resolution level obtained just after one wavelet decomposition by modifying the orientations and norms of the wavelet coefficient vectors; the high-capacity watermark is inserted in one or several intermediate levels by considering groups of wavelet coefficient vector norms as watermarking primitives. Experimental results demonstrate the effectiveness of the proposed framework: the robust watermark is able to resist all common geometric attacks even with a relatively strong amplitude; the fragile watermark is robust to content-preserving operations, while being sensitive to other attacks of which it can also provide the precise location; the payload of the high-capacity watermark increases rapidly along with the number of watermarking primitives.