The dome of the Florence Cathedral (Santa Maria del Fiore), designed by Filippo Brunelleschi and constructed between 1420 and 1436, was an engineering marvel of its time. Its construction involved several innovative techniques due to its immense size and the fact that traditional centering (wooden support framework) for such a large dome was not feasible.
Key innovative techniques used by Brunelleschi:
Double-shelled dome (Option c): The dome consists of two shells: an inner structural shell and an outer protective shell, with a space between them. This design reduced the overall weight of the dome and provided access for maintenance. The inner shell is thicker and bears more load.
Ribbed construction: The dome is octagonal and has eight primary stone ribs (and sixteen intermediate ribs) that rise from the drum to the lantern. These ribs provide the main structural framework.
Herringbone brick pattern (Spina Pesce): Brunelleschi used a special herringbone pattern for laying bricks in the dome shells. This helped to lock the bricks together and distribute stresses as each course was built, allowing the dome to be self-supporting during construction without massive centering.
Tension rings: Horizontal reinforcement rings (made of stone, iron, and wood) were incorporated within the dome structure at various levels to counteract the outward hoop stresses (thrust) that tend to push the dome apart.
Innovative hoisting machinery: Brunelleschi designed special cranes and hoisting machines to lift heavy materials to the great heights required for dome construction.
Let's evaluate the options:
(a) Flying buttresses and ribbed vaults: These are characteristic features of \textit{Gothic architecture}, which predates Brunelleschi's dome. While the cathedral itself has Gothic elements, Brunelleschi's dome design was a departure, inspired by classical principles and innovative engineering. The dome was designed to be self-supporting without external flying buttresses. Ribbed vaults are used in Gothic ceilings, not directly the innovative technique for this specific dome shell structure.
(b) Pointed arches and stained-glass windows: These are also characteristic of Gothic architecture. Brunelleschi's dome has an ogival (pointed) profile, but "pointed arches" as a general Gothic feature is not the primary innovative technique for its construction. Stained-glass windows are in the drum, not a construction technique for the dome itself.
(c) Double-shelled dome with an inner and outer layer: This was a key and innovative structural solution employed by Brunelleschi to manage the weight and construction of the massive dome.
(d) Extensive use of iron and steel framing: Iron was used for tension chains/rings within the masonry dome, but "extensive iron and steel framing" as a primary structural system is characteristic of much later 19th and 20th-century architecture (e.g., Crystal Palace, Eiffel Tower, skyscrapers). Brunelleschi's dome is primarily a masonry structure.
Therefore, the most significant innovative technique for the construction of the Florence Cathedral dome was its double-shelled design.
\[ \boxed{\text{Double-shelled dome with an inner and outer layer}} \]