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It is the set of points, in 3-dimensional space, defined by the intersection of two planes which define faces of the shape.
yes
It is possible.
Since the question is unfinished, I'll assume the most obvious completion: "planes." Yes, a triangular pyramid is composed of 4 non-co-planar points which form 4 intersecting planes.
A plane midway between the two given planes and parallel to them.