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We propose a new method for sampling the rotation group that involves decomposing it into identical Voronoi cells centered on rotational symmetry operations of the Platonic solids. Within each cell, Cartesian coordinates in exponential coordinates are used to achieve almost-uniform sampling at any level of resolution, without having to store large numbers of coordinates, and without requiring sophisticated data structures. We analyze the shape of these cells, and explain how this can be used in the context of conformational searches in the fields of Robotics and Structural Biology.

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