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We propose a new set of highly descriptive local shape descriptors (LSDs) for model-based object recognition and pose determination in input range data. Object recognition is performed in three phases: point matching, where point correspondences are established between range data and the complete model using local shape descriptors; pose recovery, where a computationally robust algorithm generates a rough alignment between the model and its instance in the scene, if such an instance is present; and pose refinement. While previously developed LSDs take a minimalist approach, in that they try to construct low dimensional and compact descriptors, we use high (up to 9) dimensional descriptors as the key to more accurate and robust point correspondence. Our strategy significantly simplifies the computational burden of the pose recovery phase by investing more time in the point matching phase. Experiments with Lidar and dense stereo range data illustrate the effectiveness of the approach by providing a higher percentage of correct matches in the candidate point matches list than a leading minimalist technique. Consequently, the number of RANSAC iterations required for recognition and pose determination is drastically smaller in our approach.