This paper presents a technique for lossy compression of dense range images. Two separate compression schemes are applied. The first scheme (geometric compression) reduces redundant geometric information by generating an adaptive 3D triangular mesh that approximates the shapes present in the original range image. Geometric compression is used for obtaining an efficient representation of the range image that allows further processing. The second compression scheme (topological compression) encodes the connectivity information contained in the triangular mesh. Topological compression is used for generating a compact representation suitable to be stored or transmitted. Both compression schemes avoid costly iterative optimization algorithms. Results with real range images are presented.