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