Squinches are not a rare type of octopus; they are not an excruciating face pulled after eating a bitter olive1; nor are they a type of sponge for washing your auld lobby down. They are in fact an obscure feature of Roman and early Byzantine architecture, a small arch to hold up a dome.
The Romans inherited their architecture from the Greeks, who built everything using vertical columns with horizontal lintels across the top. The Egyptians before them had used similar construction methods. The lintel is structurally inefficient - there is a huge stress on it just at the point where it meets the column, and lintels often crack at this point. This is prevented by narrowing the spacing of the columns. Greek and Egyptian temples, particularly the big ones, were a forest of close spaced columns to hold up the roof.
The Romans invented the semicircular arch, which spreads the load more evenly, so the gap between the columns can be widened, allowing much more spacious buildings.
Where an arch is extended widthways to form a roof in the shape of a half-cylinder, we have what is known as a barrel vault. This was often used to cover a rectangular space, with the sides of the vault resting on the two long walls of the rectangle.
The ultimate example of a barrel vault is Persian rather than Roman: the palace of Ctesiphon, the Persian capital, has an enormous barrel vault which is still standing: roughly parabolic in shape rather than semicircular, it is 110 feet high and covers a room 80 feet by 160 feet in size.
A double barrel vault or groin vault is more elaborate: two half-cylinders are placed at right angles, intersecting over the middle of the room and forming a cross shape with four equal arms. This was used in some early Christian churches, since these favoured the cross shape.
Along with the arch, the Romans invented the dome, which can be thought of as a super-arch: it is arch-shaped whichever way you look at it. The dome allowed a much wider roof to be built than barrel vaulting, so much bigger temples could be built.
The ultimate example of the Roman dome must be the Pantheon in Rome. This temple to all the gods has a giant concrete dome, the biggest ever built in classical times and not bettered until 1420, when the cathedral in Florence was constructed. The Pantheon's dome is in fact still the biggest one ever made out of mass concrete.
Along with the circular dome comes the problem of how to stand a circular dome on a rectangular building. In the Pantheon, the whole temple is circular. The circular outer wall is very thick and it supports the weight of the dome at all points around the perimeter. But the Romans didn't want to always make their temples circular: a nice square or rectangular shape would be much more efficient.
The Pantheon was the last great pagan temple to be built in Rome. In the 4th Century, the Roman Empire became officially Christian, and from then on, the architects built churches. But the architectural problems were the same.
If you build your church as a square, with four equal walls, then you can balance your dome on top of it, and the dome will rest on the walls on just four points. Because the weight of the dome is only on these points, you can replace each of the four walls with a semicircular arch, and the dome will sit on top of the apexes of the four arches. If you want it taller, you just stand the four arches on four thick columns, one at each corner of the square.
Enter the Squinch
Of course, the dome should be supported in more than four places. The first solution to this problem was the squinch - the idea was probably borrowed from the Persians. This is a small arch which is at 45 degrees to the main arches, and sits across the corner, resting on two of the main arches. The top of the squinch is at the same level as the tops of the main arches. There are four squinches, one in each corner of the square. This means there are now eight points all at the same height which can be used to support the dome.
Squinches were used on many of the early Christian churches, which are known as early Byzantine rather than late Roman2. Bigger churches could be built by making a number of square sections which were stuck together to make whatever shape was necessary. Each square section would be roofed by a dome standing on four main arches and four squinches.
Variants of the Squinch
Although the squinch started out as a simple arch at 45° to the main arches, various versions of it were developed. A number of arches of different sizes can be used to fill in the corner, or a 'corbelled' structure consisting of flat slabs of stone set into the side walls, and each layer sticking out slightly further than the one below it. Such squinches were easy to make and required no great carving of the stone into fancy shapes, so they were popular in Western Europe in the Middle Ages long after they had been abandoned in the East.
The Squinch is Superseded by the Pendentive
The squinch was sufficient for small churches, but as the Byzantines wanted to build bigger and bigger buildings, the need for bigger domes became evident. A dome sitting on only eight supports was structurally weak. Something better was needed. In the 6th Century, the 'pendentive' was invented. Again the dome was placed on top of four arches around the four sides of a square space. But instead of adding squinches to the four corners, the gaps between the arches and the bottom of the dome were filled with curved surfaces known as pendentives. These were sections of a bigger sphere, so they acted like domes themselves, distributing the weight from above evenly onto the arches.
The first place where this technique was used was in the church of Hagia Sophia in Constantinople, to great effect, making it one of the most impressive buildings of the ancient world. Pendentives subsequently became the standard method of attaching a dome to a square base, used in such great buildings as St Mark's Basilica in Venice, St Peter's Basilica in Rome and St Paul's Cathedral in London.
The pendentive, being a smooth surface, is very suitable for the application of mosaics. A favourite subject of the Byzantine artists for the four corners of the square were pictures of the four evangelists, the men who had written the four gospels. These were symbolically represented by a man (Matthew), a lion (Mark), an ox (Luke) and an eagle (John).
Admission of Guilt
Actually, we lied to you. In America, the word 'squinch' has been used since the 19th Century for a facial expression which is a cross between a squint and a pinch. So a squinch is, in fact, also an excruciating face pulled after eating a bitter olive!