On a recent trip to China, I visited Tiananmen Square in Beijing and was struck by the similarities between the buildings flanking it on the east and west and those built in Nazi-Germany or the Soviet Union to house state functions. The similarities between the latter two were already skewered by Osbert Lancaster in his collection of architectural cartoons Pillar to Post (1938; top two drawings on the left). The Great Hall of the People at Tiananmen Square (bottom left) would have provided him with a third example.
All of these are instances of Herrschaftsarchitektur. Herrschaft is a general term that can refer to any situation in which someone is Herr (in the sense of "master" or "lord") over someone or something else, like the rule of a certain party or the reign of a certain leader. And Architektur is, of course, a cognate of English "architecture".
Herrschaftsarchitektur, then, refers to the buildings a ruling class or party erects to accommodate its operations and, at the same time, express its power and dominance. The latter characteristic is essential: To become Herrschaftsarchitektur, it's not enough that a building be used by a ruling power. It must be intended to symbolize its might and will to rule, often in combination with an attempt to intimidate its subjects.
Follow-up: Public Architecture in China Today.
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