Reuleaux triangle
Architecture

In Gothic architecture, beginning in the late 13th century or early 14th century, the Reuleaux triangle became one of several curvilinear forms frequently used for windows, window tracery, and other architectural decorations. For instance, in English Gothic architecture, this shape was associated with the decorated period, both in its geometric style of 1250–1290 and continuing into its curvilinear style of 1290–1350. It also appears in some of the windows of the Milan Cathedral. In this context, the shape is sometimes called a spherical triangle, which should not be confused with spherical triangle meaning a triangle on the surface of a sphere. In its use in Gothic church architecture, the three-cornered shape of the Reuleaux triangle may be seen both as a symbol of the Trinity, and as "an act of opposition to the form of the circle".

The Reuleaux triangle has also been used in other styles of architecture. For instance, Leonardo da Vinci sketched this shape as the plan for a fortification. Modern buildings that have been claimed to use a Reuleaux triangle shaped floorplan include the MIT Kresge Auditorium, the Kölntriangle, the Donauturm, the Torre de Collserola, and the Mercedes-Benz Museum. However in many cases these are merely rounded triangles, with different geometry than the Reuleaux triangle.
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