Page 16
Tower Relocation
The plant minor diagonal intersection is closer to the façade wall by the measure e (m+n), following the tower enlargement. The intersection of the minor diagonals marks the cross vault location, which in turn defines the room width in the plant design geometric algorithm.
As a result, the room width has been reduced by the measure 2e.
In order to restore the room width to the measure defined in the concept design, the measure w, a consideration is to relocate the façade wall by the measure e outward along the plant side direction.
Per the geometry of triangle T_{7}, folio 113:06, a move by the measure e in the plant side direction corresponds to a move by the measure i in the plant corner direction, folio 116:01.
Accordingly, the tower and footing octagon are relocated as a unit along the plant corner direction by the measure i, folio 116:01.
The references to the tower and footing corners are distinguished with the doubleprime superscript (") after the tower relocation. These corners occupy new positions with respect to the concept design frame, although their relative interdisposition has not changed.
The façade wall is attached to corners B', H' and AA', and is relocated outward with the tower relocation. The façade wall width does not change, but the length of this wall between adjacent towers is slightly longer.
The result is that the separation j" between the façade wall and the intersection of the minor diagonals anchored at corner E is returned to the measure established in the concept design, folio 116:01.
j” = j’ + (m+n) = j  2n  (mn) + (m+n) = j  2n  m + n + m + n = j
This means that the room width is similarly returned to the measure established in the concept design.
The plant minor diagonals whose intersection satisfies the room width are not the new ones that can be drawn from corners E", but the ones anchored at corner E' of the tower enlargement, which corresponds to corner EE in the concept design, folio 116:02.
With the tower relocation, these minor diagonals intersect the façade wall outdoor face at point M, folio 116:02.
This point M marks the corner of the open space triangle that is the corner notch; it lines up with the side of the tower octagon, folio 116:02.
This means that if the corner notch is filled with masonry, the minor diagonals anchored at corner E', which is the same as corner EE, satisfy two criteria: (1) they pass through the critical corner M, the point at which the tower is attached to the façade wall; and (2) they form an intersection that is at the distance j from the façade wall, folio 116:02.
The tower relocation is thus successful in resolving the final issues raised by the tower enlargement.
The tower redesign has accomplished the goal of enlarging the tower while staying within the framework and structural solutions laid out in the concept design, folio 116:03.
The geometric changes have included a slight redefinition of the façade wall and a small relocation of the new enlarged tower, all performed using the quantum geometric forms of the feature triangle.
The design is returned to the specifications made in the concept design with respect to:

The façade wall width

The room width

Lateral thrusts that are contained within the concept design footprint, footing corner EE

Cross vault at the intersection of plant minor diagonals

Plant minor diagonals that cross from the façade wall to the tower at the critical corner M, with no corner notches
The plant octagon radius (half of the major diagonal) increases by the measure i with the tower relocation. Combined with the tower enlargement that adds the measure k, the overall increment in the plant radius is k+i The façade wall has moved by the amount e , folio 116:03.
These are minor adjustments considering that both k and i are a function of f, which is 0.38 meter. The radius estimate of the plant is about 28 meter. The increment in the plant radius is less than 2%, a very small change.