The rotation diagram and optimal containing placements of a convex polygon

Consider placing a convex polygon P in contact with a point z in the plane. We can rotate P around point z; we can translate P “around” 2 keeping the boundary of the polygon in contact with the point; or we can do a combination of both. The rotation diagmm Rp,= is a rectangular diagram representing the configuration space of these possible translations and rotations. The configuration space is given as follows: