During the last fifteen years of his life, Gaudí planned many parts of the church so that they could be built in the future. He did so combining geometrical forms, chosen for their formal, structural, luminous, acoustic and constructive qualities: hyperboloids, paraboloids, helicoids, conoids and ellipsoids. Many of these surfaces are ruled, which makes the construction easier. He assigned one of these forms to each type of the elements that make up the naves. With helicoids he invented a new column in the history of architecture: the double twisted column. He used hyperboloids for the openings of the windows and the vaults. With paraboloids he created linking surfaces on the vaults, the roofs and the columns of the Passion façade. He generated the knots or capitals of the main columns with ellipsoids. And earlier he had planned the building of the parish schools with conoids.
Moreover, Gaudí developed a system of proportions applied to all the dimensions and elements of the church.
DOUBLE TWISTED COLUMN
HELICOID AND CONOID