Suppose $P$ is a convex lattice polytope in $Z^3$ without interior lattice points, and we require the interior lattice points of each facet(i.e. dimensional 2 faces) are neither too much nor too few, say, they are less or equal to 2 but bigger or equal to 1.
Is there any classification results on such polytopes? Are there finite such polytopes, or is there any known method can be used to deal with such polytopes? Any suggestions, remarks, references for the problem or similar questions are great appreciated!