Construction of the high gallery and both towers of the façade
During this period, the high gallery and the two towers over the façade were built. The high windows were modified and enlarged, and the side chapels were developed. See the inside of the towers, which are now closed for visitation, on the videos below:
The design, however, was continuously revised during the course of construction. For example, in the 1220s the upper wall of the cathedral, which had already been constructed, was demolished and rebuilt to allow for larger windows. This transformed the building from a four-story to a three-story structure.
The new cathedral was largely completed by around 1245, although, construction continued in various parts until the mid-14th century. During these 200 years chapels were added along the exterior of the cathedral, some structural supports modified and the transept arms were extended, giving the cathedral a cross-like shape.
In my assessment, these many remodels during the Middle Ages demonstrated the vitality of the cathedral in medieval life and the creativity of the builders, as they adapted the building to changing architectural fashions and social practices. The change to a three-story structure, that had become the standard by the early 13th century, is one such example. — Maile Hutterer for The Conversation