Neural Fields (NFs) have gained momentum as a tool for compressing various data modalities - e.g. images and videos. This work leverages previous advances and proposes a novel NF-based compression algorithm for 3D data. We derive two versions of our approach - one tailored to watertight shapes based on Signed Distance Fields (SDFs) and, more generally, one for arbitrary non-watertight shapes using Unsigned Distance Fields (UDFs). We demonstrate that our method excels at geometry compression on 3D point clouds as well as meshes. Moreover, we show that, due to the NF formulation, it is straightforward to extend our compression algorithm to compress both geometry and attribute (e.g. color) of 3D data.