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Our world is known for its abundance of symmetric structures - in the fields of the animal kingdom, in astronomy, mathematics and chemistry, to name a few. The existence of symmetry in 3D shapes is of great interest when such applications as efficient storage, comparison and lookup are considered. Traditionally, only symmetries which are a composition of rotations and reflections were considered. These symmetries, termed extrinsic, have limited use in non-rigid shapes, as they are easily lost when the shape is deformed. A different approach, treating 3D shapes as metric spaces, allows the definition of intrinsic symmetries, which offer a way for symmetry detection in deformable, non-rigid shapes. In this work we present a method to compute intrinsic, continuous symmetries of 3D shapes, based on a general-purpose isometry-finding algorithm. We further explore non-Euclidean intrinsic continuous symmetries, and in particular, we demonstrate an algorithm for the detection of affine-invariant intrinsic continuous symmetry.