Cloister vault

A Cloister-vault, or domical vault, is a vault resulting from the intersection of two barrel-vaults crossing in a right angle.

Geometry

The intersection of the cloister vault with a horizontal plane is a square. This fact may be used to find the volume of the vault using the slicing method of Integral calculus. Finding the volume in this way is often an exercise for first-year calculus students.

Assuming the intersecting barrel-vaults are semi-cylindrical, the volume of the vault is $\frac{1}{3}s^3$ where s is the length of the side of the square base.

Examples

The chapel of the Portuguese Cardinal (James of Lusitania), in the Basilica di San Miniato al Monte, Florence, Italy
Side chapels in the Church of St. Ippazio, Tiggiano, Italy
Maple Leaf Gardens Roof
Moscow Orphanage Roof of the Central Administrative Building