Façade Wall Redefinition
The new footing corner HH' is almost as distant from the indoor face of the façade wall as the corner H; the latter is the anchor of the façade wall outdoor face in the concept design, folio 113:01.
The same is true for corner BB' whose distance from the indoor face of the façade wall is the same small difference shorter that the distance of corner B from the indoor face of the façade wall, folio 113:01.
Furthermore, corners BB' and HH' make clean geometric anchoring points for the façade wall, folio 113:01.
The solution, therefore, is to redefine the anchoring corner for the outdoor face of the façade wall to corners BB' and HH' of the enlarged footing octagon, folio 113:02.
The resulting wall thickness is smaller that the measure in the concept design. The task next is to measure the reduction and find an adjustment to return the façade wall thickness to the measure defined in the concept design.
Measurement of the Façade Wall Reduction
The footing corner triangle is instrumental in providing a measure of the reduction in the façade wall thickness, folio 113:03.
An enlarged view of the area of interest is provided in folio 113:04 for improved clarity. The footing corner triangle is referred to as triangle T1 and is the feature triangle.
Recognizable in the footing corner triangle are the geometric shapes created by the existing lines as they cross trough the footing corner. Prominent is the right-angle triangle T2 and the equal triangle T4.
These are easily recognized as the geometric sub-components of the footing corner triangle, which is in the form of the feature triangle.
The feature triangle is of special interest in geometry and was studied in the previous design phase. Folio 113:05 provides a summary of the special study made of this unique triangle. Folio 113:06 provides an application of these features to the footing corner triangle.
The geometry of the sub-component triangles in the footing corner triangle provides a mathematical definition of the reduction in the façade wall thickness, folio 113:04.
This reduction is the measure m-n; it is in the range of 4 to 5 centimeter in the final construction.
The medieval architect’s remedy to make up for this wall reduction was to add a finishing layer of the thickness m-n to the indoor face of the façade wall, folio 113:07.
There are now two references for the indoor face of the façade wall:
A stone face that smoothly and continuously flows into the vault stonework at the spring line and is anchored to corner AA, which is relabeled corner AA' following the tower enlargement.
A finishing face that rises from floor to the vault spring line.
The finishing face serves to cover the walls with marbles and other artistic details and is marked off by a cornice at the spring line.
There is clear evidence of these two surfaces, folios 113:08 and 113:09. Most of the finishing layer has disappeared over the centuries. What is observable nowadays is the stone face and the stone cornices embedded in the stone wall that framed the finished portion, folio 113:08. There are some remnants of the finishing layer still visible, folio 113:09.
The focus in this design phase is the form layout and the structural solutions; the design of architectural and artistic feature came later in the process.
With this redefinition, the façade wall thickness is returned to the measure determined in the concept design, following the tower enlargement. The remaining problem is the minor diagonals and the cross vault location.