This paper deals with the problem of analyzing and visualizing volume data sets of large size. To this aim, we define a three-dimensional multi-resolution model based on unstructured tetrahedral meshes, and built through a half-edge-collapse simplification strategy, that we call a Half-Edge Multi-Tessellation (MT). We propose a new compact data structure for a half-edge MT, and we analyze it with respect to both its space requirements and its efficiency in supporting Level-Of-Detail (LOD) queries based on selective refinement.