Polygonal domes, such as the eight-sided dome of Santa Maria del Fiore, are more complex in their design than round domes, which are generated by rotating a quarter-circle around a vertical axis.
To build a dome without the use of a supporting framework, each of the masonry rings that compose the dome must be completed in succession.
This was the method used by Brunelleschi, and illustrated in the model of the masonry layers. The bricks were laid on sloping beds. Before closing each ring of bricks, the workmen placed a row of bricks whose longer sides protruded with respect to the bricks resting on the conic surface. This arrangement, known as a herring-bone, displays a spiral profile.
The second model shows the geometric principles of Brunelleschi?s dome and illustrates two other essential features.
First, we can see the method used to obtain the so-called pointed-fifth curvature of the angle ribs. Brunelleschi took the circle in which the dome's inner octagon is inscribed, and divided it into five equal parts. He then traced intersecting arcs with a compass opening equal to four-fifths of the circle?s diameter.
Second, the model shows the characteristic profile of the brick beds, known as "slack line" because it resembles a loose string. The reason for this is that the brick beds all lie on the surface of an inverted cone whose axis coincides with that of the dome. The cone?s vertex shifts upwards as the work proceeds.
This construction method is comparable to what happens when we use a pencil sharpener. The polygonal pencil is the equivalent of the dome, while the cone-shaped opening of the device represents the dome?s inverted cone design. The sharpener turns the pencil's vertical sides into conic surfaces.