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In America Thomas Jefferson's design for the University of Virginia centered the housing and academic buildings around the Lawn, a huge grassy expanse. Later American college and university planners imitated either the Jeffersonian plan, the Oxbridge idea, or a combination of the two.
Despite the obvious relationship of the word "quadrangle" to the number 4, architects do not feel bound by a strict numbering of sides.
The word "quadrangle" is also sometimes, but not very often, used to mean a quadrilateral.