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In this paper we present an approach for creating complete shape representations from a single depth image for robot grasping. We introduce algorithms for completing partial point clouds based on the analysis of symmetry and extrusion patterns in observed shapes. Identified patterns are used to generate a complete mesh of the object, which is, in turn, used for grasp planning. The approach allows robots to predict the shape of objects and include invisible regions into the grasp planning step. We show that the identification of shape patterns, such as extrusions, can be used for fast generation and optimization of grasps. Finally, we present experiments performed with our humanoid robot executing pick-up tasks based on single depth images and discuss the applications and shortcomings of our approach.