A squinch in architecture is a construction filling in the upper angles of a square room so as to form a base to receive an octagonal or spherical dome. Another solution to this structural problem was provided by the pendentive.

Squinches may be formed by masonry built out from the angle in corbelled courses, by filling the corner with a vise placed diagonally, or by building an arch or a number of corbelled arches diagonally across the corner.

The tubes are arranged according to their position:

Trunk in the corner: which leans on two sections of wall forming a re-entrant angle;
Trompe in the corner: which is supported on two sections of wall forming a salient angle, in crown of a cutaway.

History in the Middle East
The dome chamber in the palace of Ardashir, the Sassanid king, in Firuzabad, Iran is the earliest surviving example of the use of the squinch, suggesting that the squinch may have been invented in Persia. After the rise of Islam, it was used in the Middle East in both eastern Romanesque and Islamic architecture. It remained a feature of Islamic architecture, especially in Iran, and was often covered by corbelled stalactite-like structures known as muqarnas.

History in Western Europe
It spread to the Romanesque architecture of western Europe, one example being the Normans’ 12th-century church of San Cataldo, Palermo in Sicily. This has three domes, each supported by four doubled squinches.

The word squinch comes from the Persian word “سه+کنج) “سکنج) (sekonj).[not in citation given] Or possibly, as the Oxford English Dictionary says, it comes from the French word “escoinson,” meaning “from an angle” which became the English word “scuncheon” and then “scunch”.

In popular culture
The science fiction novel Implied Spaces by Walter Jon Williams uses squinches as an example of parts of a structure whose construction is implied and made necessary to facilitate the construction of other parts; areas of a created world or universe which are implied (and thus created) as a by-product of the creation of other areas.

Dome on horns
The technique of the cupola on horns is one of the two main techniques (with the dome on pendants) which allows to suspend a dome with round or octagonal base above a square space which circumscribes it. The trunk is the most primitive and simplest technique to perform, but it allows to hang only small domes with good wall thickness. The pendant, however, more complex to achieve, can significantly expand the diameter of the dome. the tubes may, however, be subdivided and compounded to be closer to the shape of a pendant, so the two techniques may sometimes be related.

The dome on horns was known to the Romans since ancient times. Although the still standing Roman examples that have survived to this day are late, the presence of square spaces that seem to have been covered by cupolas suggests that the technique was known very early. One of the finest examples is the dome of the early Christian baptistery San Giovanni in Fonte of Naples, whose cupola and trunks are covered with mosaics of the fifth century (baptistery construction however began in the fourth century). The rather common motif of “shell” found on Byzantine horns, Islamic and Romanesque, is typically Roman (decorations of “cul de four” and eardrums in Roman architecture) and could be an index of sources of inspiration antique. The oldest known example of a cupola on a trunk, which is still partially standing, is found in Sasanian architecture, in the Ardashir Palace dating back to the 3rd century, a monument which has some Roman influences elsewhere.

This technique is widely used in Byzantine and Armenian architecture. In the Byzantine architecture this technique will be quickly competed by the pendants, close in appearance but it is actually a very different and more subtle technique, distributing the thrusts of the dome much more directly and homogeneously than the tubes on four pillars around the square space to cover, and therefore more suited to large domes. The Saint Sophia Basilica in Constantinople is the most striking example. While the tubes must rest on the thick walls (these walls can themselves rest on arches to distribute the weight on four pillars). The small cupolas on trompe are also spread in the Islamic architecture where they are very frequent.

In Romanesque architecture, the dome has often been used to cover transept crossings. These cupolas are usually not very large, the transition between the square plane of the cross and the circular (or octagonal) of the dome is usually provided by simple horns. At the Sainte – Foy abbey in Conques, the trunks are used as niches housing the four statues. There are also pendants, such as the cathedral Saint-Front de Perigueux which is inspired by the large Byzantine cupolas. The builders of the Middle Ages made great use of the horns to carry the eight-sided stone spiers on the square towers (Saint-Ours de Loches Church, Saint-Denis Church of Mogneville).

The tubes are paired with claveaux, either by means of a series of concentric arches, or in the form of a cone, says Viollet-le-Duc. Islamic architecture chooses corbelled horns decorated with muquarnas.

Source From Wikipedia