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The intersection of two or more solids can either be an empty set, a point (two cones "intersecting" apex-to-apex), a line (two cubes touching along one edge), a face (two cubes, face-to-face). If the solids are "filled", the overlapping intersection will be another solid. If they are hollow, it will be a closed three dimensional figure.
A sphere intersected by two parallel planes equidistant from its centre, An ellipsoid intersected by two parallel planes equidistant from its centre, A uniform hyperboloid intersected by two parallel planes equidistant from its centre, A torus with a wedge removed, A cylinder.
If it is two parallel side, rather than two pairs, then it could be a right angled trapezoid, a rectangle or a square.
The two types of solids are amorphous and crystalline solid!
They could be if they are both skew to the same line.