We will define a polytope $\Pi$ as the finite intersection of $n$ half spaces. That is, given $n$ half spaces defined by a position and a normal $P_i = (\vec p_i, \vec n_i)$, then
$$\Pi = \cap^n_{i=1}P_i$$
A polytope defined this way can be open, e.g. imagine 3 planes that intersect to form a triangular prism that extends infinitely in a direction. Or it can be closed, for example a tetrahedron.
The question is, if I give you $k$ half spaces, how do you know whether or not those $k$ form a close polytope.
A harder but also important question is, if you know they don't form a polytope, how do you find the minimum number of additional planes needed to form a close polytope along the provided one.