Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton. The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object.The symmetry set will have endpoints corresponding to vertices of the curve. Such points will lie at cusp of the evolute. At such points the curve will have 4-point contact with the circle.For a smooth manifold of dimension m in mathbb{R}^n (clearly we need m < n). The symmetry set of the manifold is the closure of the centres of hyperspheres tangent to the manifold in at least two distinct places.

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