The introduction of a thin conducting shell into vacuum changes the electromagnetic mode structure.  This modifies the zero point energy of space, so that there is an energy associated with the shape and size of the object.   The value of this Casimir self-energy has hitherto been known only for the sphere and the infinite cylinder. However,  Balian and Duplantier have given a route to its calculation for an arbitrary shape.   I will explain their method and my implementation of it, and give some examples: ellipsoid, doughnut, pancake, cucumber, and cube with rounded edges.