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The goal of this paper is to retrieve 3D object models from a database, that are similar to a single 3D object model, given as a query. The system has no prior models of any object class and is class-generic. The approach is fully automated and unsupervised. The main contribution of the paper is to improve the quality of such 3D shape retrieval, through query verification and query expansion. These are part of a cascaded, two-stage system: (i) Verification: after a first inexpensive and coarse retrieval step that uses a standard Bag-of-Words (BoW) over quantized local features, a fast but effective spatial layout verification of those words is used to prune the initial search results. (ii) Expansion: a new BoW query is issued on the basis of an expanded set of query shapes that, next to the original query, also includes the positively verified results of (i). We perform comprehensive evaluation and show improved performance. As an additional novelty, we show the usefulness of the query expansion on shape classification with limited training data and shape matching, domains in which it has not been used before. The experiments were performed on a variety of state-of-the-art datasets.