How to determine the faces of an array of points?

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Is there a way of determining the faces of any polyhedron?

I have an array of $3$-dimensional points and no information what polyhedron should come out.

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I assume that you try to compute the faces of the convex hull of your set of points. Otherwise, the given information is not enough.

Algorithmically, you could do this by applying some well-known convex hull algorithms for higher dimensions.