There have been recent efforts to learn more meaningful representations via fixed length codewords from mesh data, since a mesh serves as a complete model of underlying 3D shape compared to a point cloud. However, the mesh connectivity presents new difficulties when constructing a deep learning pipeline for meshes. Previous mesh unsupervised learning approaches typically assume category-specific templates, e.g., human face/body templates. It restricts the learned latent codes to only be meaningful for objects in a specific category, so the learned latent spaces are unable to be used across different types of objects. In this work, we present WrappingNet, the first mesh autoencoder enabling general mesh unsupervised learning over heterogeneous objects. It introduces a novel \emph{base graph} in the bottleneck dedicated to representing mesh connectivity, which is shown to facilitate learning a shared latent space representing object shape. The superiority of WrappingNet mesh learning is further demonstrated via improved reconstruction quality and competitive classification compared to point cloud learning, as well as latent interpolation between meshes of different categories.