The dome that one sees from the outside is not a vault, but a relatively light-weight wooden-framed structure resting on an invisible - and for its age highly original - catenary vault of brick, below which is another dome, (the dome that one sees from the inside), but of plaster supported by a wood frame.
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.
In the Palau Güell, there is one set of interior columns along the main facade with hyperbolic capitals. The crown of the famous parabolic vault is a hyperboloid. The vault of one of the stables at the Church of Colònia Güell is a hyperboloid. There is a unique column in the Park Güell that is a hyperboloid.
Pitched brick barrel vault In a pitched-brick vault the bricks lean (are pitched) against an existing wall. Pitched-brick vaults are named for their construction, the bricks are installed vertically (not radially) and are leaning (pitched) at an angle: This allows their construction to be completed without the use of centering.
Some ribbed vaults even have six sections in each bay (for example, the sexpartite vault, formed by the intersection of three half "barrels"). Effect of rib vaulting These advances in vaulting allowed for the addition of windows higher up in the building's walls, in the clerestory and the triforium.