Quatrefoil in the context of "Venetian Gothic architecture"

A multifoil arch (or polyfoil arch), also known as a cusped arch, polylobed arch, or scalloped arch, is an arch characterized by multiple circular arcs or leaf shapes (called foils, lobes, or cusps) that are cut into its interior profile or intrados. The term foil comes from the old French word for "leaf." A specific number of foils is indicated by a prefix: trefoil (three), quatrefoil (four), cinquefoil (five), sexfoil (six), octofoil (eight). The term multifoil or scalloped is specifically used for arches with more than five foils. The multifoil arch is characteristic of Islamic art and architecture; particularly in the Moorish architecture of al-Andalus (Iberian Peninsula) and North Africa and in Mughal architecture of the Indian subcontinent. Variants of the multifoil arch, such as the trefoil arch, are also common in other architectural traditions such as Gothic architecture. 

In heraldry, cadency is any systematic way to distinguish arms displayed by descendants of the holder of a coat of arms when those family members have not been granted arms in their own right. Cadency is necessary in heraldic systems in which a given design may be owned by only one person at any time, generally the head of the senior line of a particular family.

As an armiger's arms may be used 'by courtesy', either by children or spouses, while they are still living, some form of differencing may be required so as not to confuse them with the original undifferenced or "plain coat" arms. Historically, arms were only heritable by males, and therefore cadency marks had no relevance to daughters; in the modern era, Canadian and Irish heraldry include daughters in cadency.

A keep is a type of fortified tower built within castles during the Middle Ages by European nobility. Scholars have debated the scope of the word keep, but usually consider it to refer to large towers in castles that were fortified residences, used as a refuge of last resort should the rest of the castle fall to an adversary. The first keeps were made of timber and formed a key part of the motte-and-bailey castles that emerged in Normandy and Anjou during the 10th century; the design spread to England, Portugal, south Italy and Sicily. As a result of the Norman Conquest of England in 1066, use spread into Wales during the second half of the 11th century and into Ireland in the 1170s. The Anglo-Normans and French rulers began to build stone keeps during the 10th and 11th centuries, including Norman keeps, with a square or rectangular design, and circular shell keeps. Stone keeps carried considerable political as well as military importance and could take a decade or more to build.

During the 12th century, new designs began to be introduced – in France, quatrefoil-shaped keeps were introduced, while in England polygonal towers were built. By the end of the century, French and English keep designs began to diverge: Philip II of France built a sequence of circular keeps as part of his bid to stamp his royal authority on his new territories, while in England castles were built without keeps. In Spain, keeps were increasingly incorporated into both Christian and Islamic castles, although in Germany tall fighting towers called bergfriede were preferred to keeps in the western fashion. In the second half of the 14th century, there was a resurgence in the building of keeps. In France, the keep at Vincennes near Paris began a fashion for tall, heavily machicolated designs, a trend adopted in Spain most prominently through the Valladolid school of Spanish castle design. Meanwhile, tower keeps in England became popular amongst the most wealthy nobles: these large keeps, each uniquely designed, formed part of the grandest castles built during the period.

A trefoil (from Latin trifolium 'three-leaved plant') is a graphic form composed of the outline of three overlapping rings, used in architecture, Pagan and Christian symbolism, among other areas. The term is also applied to other symbols with a threefold shape. A similar shape with four rings is called a quatrefoil.

In architecture, a foil (from Latin folium 'leaf') is a type of decorative element based on a symmetrical rendering of leaf shapes, defined by overlapping circles of the same diameter that produce a series of cusps to make a lobe. Typically, the number of cusps can be three (trefoil), four (quatrefoil), five (cinquefoil), or a larger number (multifoil).

Foil motifs may be used as part of the heads and tracery of window lights, complete windows themselves, the underside of arches, in heraldry, within panelling, and as part of any decorative or ornamental device. Foil types are commonly found in Gothic and Islamic architecture.