Shape

343 They’re Shapes before They’re Plans
This is the grid of walls
for the Villa Foscari, with an axis running through the middle column of rectangles.
Bilateral symmetry is a characteristic feature of villa plans, and it’s preserved in everything
I do.
The rooms ought to be distributed on each side of the entry and hall: and it is to be observed, that
those on the right correspond to those on the left, that so the fabrick may be the same in one
place as in the other.
I can define the grid in terms of the schema
x fi x þ xA
where x and xA are rectangles with dimensions that fit in Palladio’s system of proportions.
And the trick I used for symmetric ice-rays works perfectly again, to reflect the
schema in this way
x þ RðxÞ fi x þ xA þ Rðx þ xAÞ
so that both sides of the grid are produced at the same time. Rectangles are added
either vertically or horizontally. This is evident in two separate cases. First consider
what happens when x is on axis, so that x þ RðxÞ ¼x
Then, either xA þ RðxAÞ ¼xA, as in the rule
that builds a column of rectangles, or this isn’t so, and I have a rule