How to calculate the area and volume of a random 3d shape knowing only its coordinates?

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Given a set of 3d points which make up an vector object of any shape (with any number of points), without the edges being known, how can the object's edges be found/detected so that the object's surface 3d area and internal 3d volume can be calculated?

Note: there may be points inside the object which do not form part of the outside edges.