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In this paper we describe a novel algorithm for constructing a compact representation of 3D laser range data. Our approach extracts an alphabet of local scans from the scene. The words of this alphabet are used to replace recurrent local 3D structures, which leads to a substantial compression of the entire point cloud. We optimize our model in terms of complexity and accuracy by minimizing the Bayesian information criterion (BIC). Experimental evaluations on large real-world data show that our method allows robots to accurately reconstruct environments with as few as 70 words.