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Wouldn't you need a little material "left over" to claim that it can pass through itself? Two spheres of equal size wouldn't work because they would occupy exactly the same space.
Yes!
The "pass through itself" criteria is the same as "has one shadow that fits entirely inside another shadow". If you allow "one shadow equals another shadow" then it's trivially true for every shape because a shadow equals itself.
Note that this "shadow" language assumes a point light source at infinity, i.e. all the rays are parallel.