Step 1: Hyperboloid.
\nThe Cathedral of Brasilia, designed by Oscar Niemeyer, features a distinctive hyperboloid form. \n\[\nP \Rightarrow 5\n\] \n\n
Step 2: Geodesic Dome.
\nThe Biomes at the Eden Project in the UK utilize geodesic dome constructions, engineered by Nicholas Grimshaw. \n\[\nQ \Rightarrow 3\n\] \n\n
Step 3: Diagrid Structure.
\nThe Hearst Tower, New York, a Norman Foster design, stands as a prominent instance of diagrid structural systems. \n\[\nR \Rightarrow 4\n\] \n\n
Step 4: Umbrella Structures.
\nPalazzo del Lavoro, Turin, by Pier Luigi Nervi, incorporates umbrella-style roof structures. \n\[\nS \Rightarrow 2\n\] \n\n \n\[\n\boxed{P-5, \ Q-3, \ R-4, \ S-2}\n\]