Though many of these architects are known for either their prairie or organic styles, Wright designed the Guggenheim.

The Chrysler Building in New York City is a well-known example of the Art Deco artistic and architectural style. Art Deco is known for its bold, geometrical shapes, rather than the organic, flowing style of Art Nouveau, or the Greek-and-Roman-derivation of Neoclassicism. Art Deco was not intricate or natural. It embraced technology and the modern world, and reflected the glamour and luxury that modern technology provided. 

The Chrysler building is a good example of Art Deco architecture, as its spire is composed of symmetrical, bold, powerful geometrical shapes. It also makes sense that Art Deco, which represented glamour and luxury, would be used in that time period to build a skyscraper in New York, which in and of itself is a representation of the modern world.

Rococo and Gothic architecture are not from the 20th century.

Image accessed through Wikipedia Image Commons: https://commons.wikimedia.org/wiki/File:Chrysler_Building_by_David_Shankbone_Retouched.jpg

Frank Lloyd Wright built Fallingwater outside of Pittsburgh in 1935 for the owner of a Pittsburgh department store, Edgar Kauffman. Kauffman desired a specific, small plot of land to be used and wanted very specific elements. In order to build a large house in a tight space, Wright used a revolutionary cantilevered approach in his design, also incorporating natural elements like a waterfall, giving the building its name.

The long, low Robie House which Wright created to match its prairie setting is a good example of how he matched design to fit surroundings. He felt the building should make the area even more beautiful than before its construction. His "Fallingwater" house in PA is another example of architecture matching its setting.

While Fallingwater is a thoroughly modern building, constructed in straight lines made out of concrete, glass, and steel, Frank Lloyd Wright was heavily inspired by Japanese architecture. Fallingwater was designed as a natural retreat for its owners, which meant Wright had to carefully blend the house into nature. Considering its use of natural light and a sense of blending the indoor and outdoor space, the house features many approaches which are borrowed from Japanese architectural ideas.

Le Corbusier was both a practicing architect and an architectural theorist. These two identities were best joined in his design and construction of Villa Savoye outside of Paris. The building intentionally and forcefully followed Le Corbusier's manifesto Five Points of Architecture. The five points Villa Savoye followed were having pilotis that lifted the building off the ground, a functional roof that could be used as a garden, a free floor plan without load bearing walls allowing interior openness, large windows that provided vast amounts of natural light, and freely designed facades that acted merely as a skin on the outside of the building.