A fan vault is a form of vault used in the Gothic style, in which the ribs are all of the same curve and spaced equidistantly, in a manner resembling a fan. The initiation and propagation of this design element is strongly associated with England.
Fan vaulting over the nave at Bath Abbey, England: made from local Bath stone, this is a Victorian restoration (in the 1860s) of the original roof of 1608
Bath Abbey
King's College Chapel, Cambridge
Canterbury Cathedral
In architecture, a vault is a self-supporting arched form, usually of stone or brick, serving to cover a space with a ceiling or roof. As in building an arch, a temporary support is needed while rings of voussoirs are constructed and the rings placed in position. Until the topmost voussoir, the keystone, is positioned, the vault is not self-supporting. Where timber is easily obtained, this temporary support is provided by centering consisting of a framed truss with a semicircular or segmental head, which supports the voussoirs until the ring of the whole arch is completed.
Gothic rib vault ceiling of the Saint-Séverin church in Paris
In a pitched-brick vault the bricks lean (are pitched) against an existing wall.
St Paul's Cathedral Choir looking east, London
Pointed barrel vault showing direction of lateral forces