Rules · Cities · Walls · Plans · Geometry
Give a new city a regular polygonal outline with a bastion at every angle, put the principal piazza at the centre with the chief church and the seat of government on it, and distribute lesser squares for the markets through the quarters.
Scamozzi’s Idea (1615) sums up a century of Italian thought about the new city. His own ideal plan is a twelve-sided fortress whose streets form a grid inside the bastioned ring, with a great piazza at the centre for the cathedral and the palace, secondary squares for the different markets, and a canal through the middle. The Venetian fortress of Palmanova (1593), with which Scamozzi was associated, shares the regular polygon, the bastions and the central piazza, but runs its streets radially from the centre.
The attribution of Palmanova’s plan is disputed: Giulio Savorgnan and other military engineers of the Republic directed the works, and Scamozzi’s part is uncertain; the gates and the cathedral are the works most often given to him.
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
In a row of arches the thrusts of neighbouring arches cancel over each intermediate pier, which may therefore be slender; at the ends of the row nothing balances them, so the outermost piers must be made wider or buttressed.
To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.
sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2
If the sphere that forms the pendentives is simply continued above the ring, the bay is covered by a single shallow dome, the sail vault or pendentive dome, which springs directly from the four corners.
crown = h₀ + S⁄√2 (lower than a hemisphere on the ring, h₀ + S)
Give the villa garden porticoes for sun and for shade, grottoes made in imitation of nature with tufa and shells, evergreens planted in straight rows at equal distances, and hedges of box; set vines on columns over the walks.
Lay the ideal garden out on a circular plan in concentric rings, woods outside, then meadows and orchards, then gardens of knots and clipped evergreens divided by walks, with water and the fountain of the goddess at the centre.
Cite this page Chris Paton, “The fortified city as a regular polygon”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/scamozzi-ideal-city. Text, drawings and models licensed under CC BY-NC 4.0.