The word quatrefoil etymologically means "four leaves", and applies to general four-lobed shapes in various contexts.
In architecture and traditional Christian symbolism, a quatrefoil is a symmetrical shape which forms the overall outline of four partially-overlapping circles of the same diameter. Two common types of quatrefoil are shown in the first two images below (click on the images for larger illustrations, and explanation of the geometry involved):
The quatrefoil enjoyed its peak popularity during the Gothic Revival and Renaissance, but can still be seen on countless churches and cathedrals today. It is most commonly found as tracery, mainly in Gothic architecture, where a quatrefoil can often be seen at the top of a Gothic arch, sometimes with stained glass on the interior.
In art, the quatrefoil is a type of decorative framework (mainly used in engraving), consisting of an architectural quatrefoil combined with a square (just as the trefoil is often combined with an equilateral triangle), as seen in the image on the right above. Among the most famous works of art employing the quatrefoil are bronze panels on the North Doors of the Baptistery in Florence by Lorenzo Ghiberti (also Filippo Brunelleschi's equally famous competition entry for the same doors, The Sacrifice of Isaac) and "Head of an Angel" by Piero della Francesca.
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