The ability to extract spatial features from 3D objects is essential for applications such as shape matching and object classification. However, designing an effective feature vector which is invariant with respect to rotation, translation and scaling is a challenging task and is often solved by normalization techniques such as PCA, which can give rise to poor object alignment. In this paper, we introduce a novel method to extract robust and invariant 3D features based on rotational symmetry. By applying a rotation-variant similarity function on two instances of the same 3D object, we can define an autocorrelation on the object in the space of rotations. We use a special representation of the SO(3) and determine significant rotation axes for an object by means of optimization techniques. By sampling the similarity function via rotations around these axes, we obtain robust and invariant features, which are descriptive for the underlying geometry. The resulting feature vector cannot only be used to characterize an object with respect to rotational symmetry but also to define a distance between 3D models. Because the features are compact and pre-computable, our method is suitable to perform similarity searches in large 3D databases.