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Irregular tetrahedral meshes, which are popular in many engineering and scientific applications, often contain a large number of vertices. A mesh of V vertices and T tetrahedra requires 48 V bits or less to store the vertex coordinates, 4·T·log 2(V) bits to store the tetrahedra-vertex incidence relations, also called connectivity information, and kV bits to store the k-bit value samples associated with the vertices. Given that T is 5 to 7 times larger than V and that V often exceeds 32 3, the storage space required for the connectivity is larger than 300 V bits and thus dominates the overall storage cost. Our "implants spray" compression approach introduced in the paper reduces this cost to about 30 V bits or less-a 10:1 compression ratio. Furthermore, implant spray supports the progressive refinement of a crude model through a series of vertex-splits operations.