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Palladio and Symmetry

Published onApr 22, 2021

One little-discussed aspect of Renaissance geometry clearly fascinated Palladio. As is often observed, all of his villa plans are laid out along a central vertical axis.1 This axis, in turn, is lined with concentric sequences or strings of spaces. On either side of these central strings the rest of the villa is constructed from room arrangements that strictly reflect each other across the central axis.

Symmetry of this sort is one of the neglected comers of architectural history. Nor is it the simple thing it is sometimes thought to be. Palladio, furthermore, employed it with a subtlety that is beyond that of his contemporaries.2 Palladio, indeed, came on the scene when the very word “symmetry” meant something different from what it means today. He was part of a movement that deprived the word of this earlier meaning and gave it its modern one. In the course of that shift, symmetry turned from a kind of measurement, and an aesthetic judgment, into a geometric technique.3 In our own time symmetry has gone on to become a branch of mathematics.

The complexities and pitfalls of symmetry were intriguing to Renaissance architects. Their study of the subject had parallels, and a possible indebtedness, to earlier postclassical art—Byzantine, medieval, and particularly Islamic. The exquisite geometries of the Timurid architecture of Iran and Turan are just one of many cases in point.4 During the Italian Renaissance, the ringleaders of the symmetry revolution were Alberti, Francesco di Giorgio, Leonardo, Bramante, and Cesare Cesariano, who seem to have been acquainted with one another’s work in the early decades of the sixteenth century in Milan.5

To the ancients the word “symmetry” meant what its components syn, “with,” and metria, “measurement,” would imply: commensuration—two things of the same size and, by extension, two or more integrated measurement systems. By further extension, in this original definition “symmetry” could mean suitable measurement, or proportion—hence beauty. For us this older meaning has been almost completely crowded out by the newer. Thus on remarking that two beams are each 6 feet long we would never say that they were for this reason “symmetrical.” Nor would we say that 6 feet is “symmetrical” with 72 inches because we use a system of measurement that has 12 inches per foot and 12 × 6 = 72 (this is what we call commensurability). But Vitruvius does exactly this: he says the “symmetries” of the Corinthian column base and shaft are the same as those of the Ionic (4.1.1), meaning that both have the same proportions and hence are the same number of diameters high. When “symmetry” came to mean what it means today, the word’s ancient association with “beautiful” probably strengthened the idea that a design with two identical halves was more beautiful than one without.

It is interesting to watch the ancients describing what we call mirror symmetry; for of course they had the thing itself even if they did not call it by that name. Theophrastus in his History of the Plants describes the beauty of foliage leaves (3.18.7; 3.12.9) using the phrase ἔυρυθμαɸύλλα, “eurhythmic leaves,” drawing on the sense of repetition we still feel in the word “rhythm.” But no dictionary of ancient Greek or Latin gives that word the meaning we give it nowadays.

As to the earliest example of “symmetry” in its modern sense, Walter Kambartel notes that when Bernini came to France in 1665 he criticized the Church of the Val-de-Grâce in Paris because one transept was of a very different design from the other. According to Chantelou, who was on the spot and wrote down the great man’s words, Bernini used the term défaut de symétrie.6 Eighteen years later Claude Perrault spoke of “our symmetry” (as opposed to the ancient sort) as the rapport d’égalité. But, Kambartel contra, Perrault never clearly states that “our symmetry” meant bilateral reflection across a central axis.7 In later books Perrault claims that symmetry means equal size, distribution, and spacing; but here again we do not really have the concept of mirror symmetry in so many words. Aside from Bernini’s phrase, we have not found any instances where the word is unambiguously employed in its modern meaning before the nineteenth century. Kambartel cites Charles Blanc’s Grammaire des arts du dessin (1867), and the Oxford English Dictionary provides an instance of about the same date.8 It is true that symmetry, in our modern sense, has always existed in nature and art, and not just in leaves. The ancients had of course observed that in a human face, a mammal’s body, and dozens of other things in nature, the left half was the mirror of the right. And ancient architects had built temples, baths, and ships that, almost more often than not, were elaborately symmetrical, precisely in the modern sense of the word. But in Western Europe, as far as we can tell, symmetry began to flourish as a geometric discipline, and indeed at times as an architectural necessity, only with the Renaissance. So the following pages on Renaissance symmetry will be discussing a science that was beginning to exist but had not yet gotten itself baptized.

1.1 Four basic types of Renaissance symmetry.

Today, symmetry is usually analyzed in terms of the main types illustrated in figure 1.1. Note that bilateral symmetry is not necessarily the same as reflective (the two upper diagrams). Bilateral symmetry consists simply of two (and not more) similar shapes on an axis. In reflective symmetry the shapes have to be mirror images of each other. There can, furthermore, be multilateral symmetry that is not necessarily reflective and reflective symmetry that involves more than one axis. Translatory or glide symmetry repeats a form axially. As to rotational symmetry, note that another way of saying that a form is rotated is to say that it changes direction, as from north to east. The change of direction is the more marked when the form is compound, when it has a strong directional axis, and when the number of axes is multiplied. In the latter case the same form now points successively north, northeast, east, and so on. In any actual design several of these types of symmetry may overlap.

In the 1460s Antonio Averlino, who adopted the scholarly sobriquet Filarete,9 produced a treatise on architecture that remained unpublished at the time but seems to have been known. It is full of symmetrical public buildings, churches, town plans, and the like. Much more unusually, it also calls for symmetry in the plans of private houses. Filarete describes a “palace for a gentleman,” for example, which, we learn from a close and patient reading of his verbal description, was to have possessed bilateral mirror symmetry.10 He begins by describing and dimensioning a central portal, then flanks it left and right with identical strings of rooms that move along the front and down the sides of a central courtyard to form the whole building into a hollow 4:3 rectangle. Unfortunately the illustrators who drew Filarete’s plan in surviving manuscripts misread the text and made the house asymmetrical. But the attentive reader can have no doubt that Filarete himself is advocating reflective symmetry across the house’s vertical axis.11

1.2 Plans from Francesco di Giorgio Martini’s Trattati di architettura, pi. 199.

1.3 Schematic diagram of Poggioreale.

In the 1480s Francesco di Giorgio Martini, a Sienese architect, sculptor, and painter, composed two illustrated architectural treatises, one a corrected and rewritten version of the other. He tells us, erroneously, that what we would call bilateral reflective symmetry ruled house design in antiquity:

The ancients employed several courtyards, some square, some of a square and a third, some of a square and a half, some of two squares, and some oval. Also their elevations were constructed in various ways, so that they were either square or one and a half squares wide; and in distinction to the square courtyards, the oval ones had circular loggias, with vaults and roofs compartmented by their ornament so that all the lines from the center might correspond; and the same thing goes for the square [rectilinear] residence.12

Francesco is lavish with illustrations of these rather opaque phrases. Among them he has a few asymmetrical house plans, but the great majority are elaborately symmetrical in the modern sense. What the diagrams tell us is that the central peristyle’s columns generate the coordinates of a grid that then shapes the rooms and other spaces grouped around that courtyard (fig. 1.2). The “center” is the courtyard and its columns. The “compartmentation” is the wall grid they generate. The automatic result is that the grid splits the left-hand half of the house into a mirror image of the right.13

We can turn now to actual buildings. Particularly crucial, for Palladio, was the villa of Poggioreale, near Naples, erected in the 1480s from a design by Giuliano da Maiano. It was probably the first consciously symmetrical domestic structure of the Renaissance. The first drawing of figure 1.3 shows the plan of the main floor (the upper floor was identical) as a set of overlapping rectangles; in the second drawing, these turn into a set of four square towers containing individual living apartments at the corners of an oblong central open court.14

1.4 Serlio’s version of Poggioreale, from his Tutte l’opere d’architettura e prospettiva (1619).

Poggioreale, which was destroyed in the eighteenth century, had been erected at the time Francesco di Giorgio was writing his treatises. He had probably seen it; the building was famous in its day and Francesco went several times to Naples in the Neapolitan royal service.15 Poggioreale’s greatest fame, however, came not from those who visited it but from the heavily revamped version of it printed by Sebastiano Serlio, which is what we reproduce (fig. 1.4).16 Serlio transformed the rectangular plan into a perfect square. This square may be described as being split into seven equal smaller squares per side. The towers are L-shaped clusters of these squares, one cluster at each corner of the large square. Set between the towers are two-story porticoes five arches wide and/or three squares long by one deep. The same module governs the interior portico and stepped central pool.

This arrangement may be thought of as a quintuple vertical split with a ratio of 1:1:3:1:1 crossed by an identical horizontal split (fig. 1.5). This means that, unlike the actual villa, Serlio’s version of the building had four identical facades. This version of Poggioreale seems to have been the first such house plan of the Renaissance. In short (as we shall see), the design had both reflective and rotational symmetry.

1.5 Serlio’s Poggioreale generated by 1:1:3:1:1 splits.

The impact of Serlio’s version of Poggioreale was immense. A whole dissertation has been written about its influence in later domestic architecture, using French examples alone!17 The scheme obviously fascinated Palladio. One of the first buildings to which his main early patron, the poet Giangiorgio Trissino, introduced the budding architect was Trissino’s Villa Cricoli.18 This had been remodeled by Trissino himself so that its main facade resembled that of Poggioreale.

The beauty of Poggioreale, to a generation that was coming to admire the play of symmetry, was that it could be interestingly disassembled and reassembled. To show this, we have concocted a second split diagram that restates the ideas in figure 1.5. In figure 1.6 the L-shaped blocks of Serlio’s scheme have arms of equal length and width. The most obvious type of disassembly or splitting here is into three parts (though double, quintuple, and sextuple splits are possible). With three-way horizontal and vertical splits, one gets a wider central axis consisting of the central square peristyle and the upper and lower exterior porticoes. Laterally flanking this axial string of spaces are two fragments that form reflective symmetries. These consist of the L-shaped apartments in the towers, two on each side of the axis. Horizontally, as noted, one gets exactly the same thing rotated 90°. We have noted the horizontal splits as A, B, and C and the vertical ones as 1, 2, and 3. Most of Palladio’s plans are based on this general idea, although most of his buildings are also oblong and hence have vertical and horizontal axes of unequal weight.

1.6 Serlio’s Poggioreale divided into a 3 × 3 grid of squares.

Serlio’s version of Poggioreale, with its four-way identical layout, is, indeed, the geometrical cousin of Palladio’s most famous villa, the Rotonda (fig. 1.7d). Once the Serlian villa’s basic constituents have been split apart, as here, it is easy to move them around, keeping them on their original axes but sliding them together or apart so as to make new plans. Thus, using the Poggioreale components of three square rooms forming an L-shaped comer (fig. 1.7a), we slide them all toward the center to create a hollow square (fig. 1.7b). The hollow center of this square can otherwise be defined as the square formed by grouping four of the basic room modules together. That inner square can then be multiplied to create four axial porticoes outside the rooms, whose columns are supplied by the four identical original porticoes on the four faces of Serlio’s Poggioreale (fig. 1.7c). Finally the central space, still four times the basic module, can be filled with a circle whose diameter is one side of that same square. Making this circle the base of a dome, we would then have converted Serlio’s Poggioreale into a respectable version of Palladio’s Villa Rotonda.19 Note that the triple vertical and horizontal splits in our scheme for Poggioreale match those in the scheme for the Rotonda. The type of manipulation we pursue here involves what is known today as glide symmetry.20

Among other built structures, one of the earliest house plans that is fully and, seemingly, consciously symmetrical in the modern sense is that of the Strozzi palace in Florence, begun in 1488. The building is generally attributed to Giuliano da Sangallo, Benedetto da Maiano (brother of the architect of Poggioreale), and an architect called Cronaca (fig. 1.8). The Strozzi plan consists, first, of a six-way vertical split whose intervals are designated by the a and b modules in the diagram. The ratio of the intervals is 5:3:5:5:3:5. There is also a four-way horizontal split whose intervals are all equal to one side of a, in other words having the ratio 5:5:5:5. As with Poggioreale, we can disassemble the plan of the Strozzi palace into L-shaped components (fig. 1.9). The four L’s are identical in size, shape, and subdivisions; each matches its neighbor when reflected across the vertical or horizontal axis. We show them stacked together (lower right) to prove this. Each is then rotated or reflected around the building’s central point in a different way. Thus, for example, if two of the clusters are removed from the stack and flipped or mirrored so as to be turned upside down, one of these can become the building’s upper right-hand comer. The other is flipped again, this time crosswise, to become the upper left-hand comer. Finally, one of the two L’s remaining in the lower right can also be flipped crosswise, which turns it into the building’s lower left-hand corner.

1.7 Transformation of Serlio’s Poggioreale into the Villa Rotonda.

1.8 Symmetries and proportions in the Strozzi palace.

This principle of mirroring and/or rotating identical L-shaped comer clusters became endemic in Renaissance architecture and was often employed by Palladio. Our computer will in effect be doing the same thing, though it does this without needing commands like “flip vertically” and “rotate 90°.”

Aside from his obvious fascination with symmetry for its own sake, Palladio also gives a practical reason for it:

The stanze [i.e., as opposed to the entry hall and sala or main hall] should be compartmented on the two sides of the entrance hall and sala; and one must warn that those on the right-hand side must correspond to, and be equal to, those on the left. Thus the fabric will be the same on one side as on the other, and the walls will take the weight of the roof equally. For if the stanze are large on one side [of the house] and small on the other, these latter will be more apt to resist the weight since the walls will be more frequent, while [the other side] will be weaker. Whence, in time, will come the greatest inconveniences, which will ruin the work.21

1.9 Generating the Strozzi palace by reflecting L-shaped room groups.

1.10 L-shaped room groups in Palladio’s Palazzo Della Torre.

In other words, symmetry is a physical necessity. An asymmetrical house will settle unevenly since one side weighs more than the other. (There is a lot of marshy ground in the Veneto.) A further inspiration, a social one, for symmetrical plans lies in the regional tradition of separate but equal apartments for man and wife, each with its salone, dining room, chamber, and other facilities.

In figure 1.10 we see how Palladio builds on the basic idea of L-shaped comer blocks that we saw in Poggioreale and the Strozzi palace. These diagrams have been extrapolated from a design in the Quattro Libri for a city house in Verona designed for a family named Della Torre.22 In the basic layout, four rectangles (marked A) measuring 36 by 20 [Vicentine?] feet,23 which is reducible to a proportion of roughly 7:4, anchor the comers of the plan. Another shape, 20 by 15 feet (whose width thus equals the height of the 7:4 rectangle), forms a 4:3 rectangle. Four of these are arranged lengthwise, flanking either end of the horizontal or minor axis, at the house’s two side entrances (marked B). Four small stairways, whose length equals the difference between the 7:4 and the 4:3 rectangles as here arranged, are tucked into the inner comers where the 7:4 and the 4:3 rectangles join (marked C). (These small rectangles are shaded to show that they are staircases.) The shaded central 2:1 rectangle in the upper row is another, much larger stair. The central lower 2:1 rectangle, in turn, forms the columned entranceway (D) leading to the villa’s central courtyard. As with Strozzi, the plan contains four L-shaped building blocks each symmetrical with the others when reflected across the horizontal or vertical axes. Alternatively, one can think of each L being rotated 180°, e.g., from the northeast to the southwest.

Other components of the Della Torre plan can be produced by interlocking and overlapping the component rectangles. To demonstrate this we assemble the 7:4, the 4:3, and the small stair into four L’s similar to those in our diagram of the Strozzi. We can now recognize this form as the plan’s basic L-shaped building block made out of the individual rectangles. This L-shape becomes the plan’s upper right-hand corner, and is then mirrored and/or rotated until the whole layout is achieved.

However when we consider the Della Torre plan simply as the result of such splits, as with Poggioreale, we run into a problem. Some of the lines created by the splitting process will have to be erased because they are not present in the finished product we are attempting to recreate. We shall see in the next chapter that there is a way of making these erasures.

Note that the vertical axes of these plans are not so much imaginary lines as concentric strings or groupings of rooms. A space the width of the 2:1 rectangle creates the vertical axis in the Della Torre plan. The horizontal axis is the width of that vertical axis minus the heights of two 4:3 rectangles. One can imagine the architect working out the plan with a single paper cutout of the L-block divided into its three component rectangles. He would simply trace that cutout into its various positions, as needed, to make the completed house plan.

1.11 Rotations of L-shapes.

Looking back at Serlio’s Poggioreale (fig. 1.5) and comparing it with the Strozzi (fig. 1.8) and Della Torre plans (fig. 1.10), we see what might be considered two different branches of rotational/reflective symmetry (fig. 1.11). When Poggioreale’s L, which has arms of equal length and width, is rotated into new positions, with each new location its arms go off in two new directions—first up and right, then down and right, then down and left, and finally up and left. But the arms of the Strozzi and Della Torre L’s are unequal. Therefore, when rotated or reflected, the longer arm always sets up a new main direction: right, down, left, up. The Poggioreale type of L is usable in central-plan buildings like the Rotonda—or for that matter Bramante’s project for St. Peter’s. The Strozzi type is useful in buildings with unequal axes such as most of Palladio’s villas—and indeed most Renaissance palaces.

The diagram in figure 1.12 illustrates twelve types of symmetry that are achievable with L-shaped blocks in which one arm is longer than the other. In each case the black L is the original block, the white L the one that has been altered. Once the possibilities for two L’s are established, one can proceed to work with larger numbers of L’s (the bottom row in fig. 1.12). One could then investigate the possibilities of L’s in which not only the length of the arms varied but also their thickness.

The medieval villa tradition of the Veneto, where most of Palladio’s houses were built, knew nothing of all this. One does find the simplest forms of translatory and bilateral symmetry here and there. But such plans are of the most rudimentary type—four identically shaped rooms in a row, for example. The other traditional types of villa or farmhouse plans in the region were asymmetrical, as Martin Kubelik has shown.24 Therefore, in designing his own villas, Palladio was probably less interested in this local vernacular than in the advanced architectural games of people like Francesco di Giorgio and Giuliano da Maiano.

1.12 Assorted combinations of L-shapes using Renaissance symmetry.


The great pioneer in rotational symmetry was Leonardo da Vinci. He should be mentioned at this point, therefore, but at the same time it should be noted that his work on symmetry was less relevant to Palladio than were such models as Poggioreale and the Strozzi palace. Leonardo’s small sketches of church plans have become famous.25 Like Palladio’s villas, Leonardo’s drawings of central-plan churches are fundamental constituents of High Renaissance and later architecture.26 But we shall see that they are, as well, simply ecclesiastical variants of the Poggioreale principle.

Most of Leonardo’s church plans involve small chapels—squares, hemispheres, and cylinders—clustering around a main central space. The churches are like planets with multiple identical moons. Sometimes the “planet” is simply a jumbo version of the “moons,” sometimes not (fig. 1.13). In the left-hand diagram, which is adapted from one of Leonardo’s sketches, we see an octagonal cappella maggiore around which an axis is rotated into eight positions, moving 45° each time. The “moon” that is rotated is a small square chapel with three apses. Note that, since the moon is in itself asymmetrical on one of its axes, its direction changes markedly every time it moves. The final church is a kind of compass rose, with a north chapel, a northeast chapel, an east chapel, and so on. The same kinds of rotation occurred with the house plans we looked at earlier. But with the Strozzi/Della Torre type there was reflection as well as rotation. With Poggioreale itself the sense of a rotation is less obvious because there are fewer instances of it. With Leonardo’s schemes, rotation becomes the most prominent feature.

In the right-hand design in figure 1.13, also adapted from Leonardo, we see the same arrangement except that at north, east, south, and west the chapels are cylindrical. Thus Leonardo not only experimented with rotational symmetry of this strongly directional type, he could deploy his components in alternating repetitions. Within these repetitions, in turn, axiality could alternate with nonaxiality, direction with nondirection. In both cases, however, and in all his other central-plan designs, Leonardo simply adds intermediate compass points to the basic north, east, south, west of the Poggioreale principle.

1.13 Rotational symmetry in one of Leonardo’s church perspectives. After Ms. B, 5v, Bibliothèque Nationale, Paris.


Filarete, Francesco di Giorgio, and the designers of the Strozzi palace and Poggioreale all belong to the fifteenth century. They knew about Vitruvius though they probably did not have an intimate and correct knowledge of his text. And even Leonardo, who lived well into the sixteenth century, had left Italy by the time the Roman author was being seriously studied in print, translated into Italian, and illustrated. The first printed Vitruvius is 1511, in Latin, and the first Italian translations (which remained in manuscript), were done some time in the following decade. Important annotated and illustrated editions appeared in 1521, 1556, and 1567.

With Vitruvius now so well established on the architectural scene, people became anxious to link him to the vogue for the new, de facto but unnamed fad for what we call symmetry. For these purposes Vitruvius’s passages on house design, while not unhelpful, required vigorous reinterpretation. Vitruvius never specifically calls for symmetrical house plans and facades. His prescriptions for what we know as symmetry are limited to public buildings, especially temples. In fact the Greek and Roman houses Vitruvius would have known were almost always asymmetrical.27 The Domus Vettiorum, Pompeii (fig. 1.14), shows the characteristic look of these ancient layouts.28 It is true, on the other hand, that, very occasionally, ancient houses were perfectly symmetrical. The so-called Casa della Farnesina in Rome, under the site of the present Villa Farnesina on the Tiber, is a case in point. But this structure was not known in the sixteenth century.29

1.14 Domus Vettiorum, Pompeii, plan. From Vitruvius’s Ten Books of Architecture, volume II, edited and translated by Frank Granger (Cambridge, Mass., 1934); reprinted by permission of Harvard University Press and The Loeb Classical Library.

Nonetheless Palladio and his predecessors made elaborate plans that endowed ancient villas and palaces with intricate plays of reflective, translatory, and other kinds of symmetry. But these drawings were really jeux d’esprit rather than serious restorations. In Palladio’s time the best way of achieving classical authority for the kind of symmetry we have been looking at was to discover it in Vitruvius—whether it was there or not.30 There are two places where Vitruvius verges on the idea that a house should be symmetrical. Speaking of house plans (6.2.1), he says: “The architect’s greatest concern is that the system governing the compartments within his buildings should be in proportion to a fixed module [rata pars].” But a house need not be symmetrical in order to be modular. Vitruvius’s subsequent discussions of domestic architecture, furthermore, fully allow for asymmetrical plans and elevations such as those of the House of the Vettii. The second point at which Vitruvius verges on a call for symmetry in domestic architecture is when he describes the atrium, which in the Roman house is a kind of antechamber to the main courtyard. Here he gives the proper length and width. There are in fact three options: the 3:2, the 5:3, and the 2:1\sqrt {2}:1 rectangles. Only the first two of these, of course, involve implicit modules (fig. 1.15). Vitruvius also prescribes height ratios for each of the three floor plans, and adds proportions for peristyles (4:3), triclinia (2:1), and exedrae (apselike niches, 1:1). Let us note that while symmetrical splitting is of course possible with a 2:1\sqrt {2}:1rectangle, using rectangular modules rather than square ones, the kind of subdivisions we see in Palladio are really only practicable with square modules and hence with rectangles such as 4:3, 5:3, etc.31

1.15 Vitruvius’s canonical proportions for an atrium.

But what Vitruvius in his text fails to say could be said for him by his annotators. In 1521 Cesare Cesariano, a Milanese architect and pupil of Bramante, produced a generously annotated and illustrated edition of Vitruvius’s text.32 He took it upon himself also to correct, or shall we say clarify and extend, Vitruvius’s prescriptions for domestic architecture. Cesare forces his author to champion symmetrical house plans in two places—once where Vitruvius talks about temples (3.1ff.) and once where he talks about houses (6.4ff.).

Book 3, chapter 1 of Vitruvius contains all sorts of geometrical rules about temple design. In his commentary, Cesare insists that here Vitruvius means to apply these rules to houses as well as to temples. (He even says they should apply to entire cities.) For, Cesare explains, when Vitruvius uses the word aedes to refer to temples, we are to recall that aedes can in fact mean any sort of building, including houses.33 What, he asks, are temples anyway but the houses of the gods? When, slightly later, Vitruvius is again writing of temples, Cesare again amends the text: “that is, temples and the houses [for the temple staff] built around them.”34

1.16 Proportions of Cesariano’s Roman house plan. After Cesare Cesariano, Di Lucio Vitruvio Pollione de architectura libri dece (Como, 1521).

When Vitruvius actually does start speaking about house plans, Cesare gets another chance to fortify his case. Where Vitruvius, as we have just seen, provides rules for a limited number of spaces but with no specified overall relationship, Cesare says that a proper house plan has to be symmetrical, in our modern sense, though of course he doesn’t use the term. How does he get away with putting these words in Vitruvius’s mouth? By yet more radical emendation. When Vitruvius starts talking about atria (6.3.3), Cesare claims that the word atrium means not only the atrium proper but the whole building. “For Ovid in the first book of the Metamorphoses says this: atria nobilium valvis celebrantur apertis, ‘the opendoored atria of the nobles [are filled with] celebrants’” (1.173). As Cesare correctly adds, classical poets by metonymy (taking the part for the whole) often called the whole house the “atrium,” usually using the plural, atria.35

When Vitruvius calls for geometrical atria, in short, he is calling for geometrical houses. Cesare is then able to print, as an illustration of the houses Vitruvius had in mind, a plan that is as symmetrical as that of Poggioreale or the Palazzo Strozzi, though it is not yet Palladian (fig. 1.16). For clarity’s sake we have transcribed only the essentials of the plan—the double grid and the main courtyards. (It is interesting that Cesare calls the plan the “symmetry” of the house. It is as if he were thinking: “symmetry—same measurements—really means: same measurements on either side of an axis.”)

Cesare’s version of Vitruvius’s Roman house, then, is an upright 5:3 rectangular perimeter split into 20-foot squares. Within this grid, and matching it, is a denser one of 10-foot squares. Hence we could call the vertical split sextuple and the horizontal split decuple. These coordinates locate all the minor rooms—wings, fauces (entrances), etc.—around the three central rectangles of peristyle, tablinum (room joining atrium and peristyle), and impluvium (open court for the collection of rainwater). Note that the central axis, as in Poggioreale and as will be the case with Palladio, is a concentric string of rooms.

1.17 Proportions of Palladio’s Roman house plan. After Vitruvius, I dieci libri dell’architettura tradotti e commentati da Daniele Barbaro, 1567 (Milan, 1987).


In 1547 Barbaro began working on his editions of Vitruvius (1556, 1567) with his own commentaries and with illustrations by Palladio.36 These commentaries carry directly on with the tendencies just discussed.37

We noted that Vitruvius had said (6.2.1) that houses should be modular, but that he supplied no example and specified no geometrical rules. To remedy this, Barbaro provides a gloss that Vitruvius would certainly never have agreed with. Following Cesare, he says that Vitruvius really meant that the modular system is the same for public buildings as for private houses. He adds that houses should in fact possess the same decorum and beauty we see in public buildings.38 Much more specifically than Cesare, therefore, Barbaro imbues house design with the proportional rules that Vitruvius gives for temples (3.1ff.). In Barbaro the ancient house is now subject to all sorts of requirements as to length, width, the play of axes, down to the smallest details of ornament. Room is made for use of temple forms—colonnades and frontispieces particularly. Indeed such things are demanded. Barbaro also makes it clear that all this is no antiquarian exercise. Modem clients were to construct and live in these symmetrized versions of Vitruvius’s domus romana.39

Palladio, Barbaro’s illustrator, goes even further. He embellishes the discussion with three views of a private palace. The first is an axial section showing the two stories of the house proper and its main courtyard, which, like a true temple, has six colossal Corinthian columns per side. The second view is the palace’s plan. This is divided into square and square-derived compartments of various sizes, which form courtyards and rooms.

The plan can therefore be measured neatly out in ratae partes as specified by Vitruvius himself. In addition, the plan conforms to the axial principles elaborated by Cesare. The central axis is one 3-module wide and eight long; the cross axis is composed of two groups of three 2-modules, one module wide; and the four intervening blocks are either 3 × 4 or 3 × 6 1-modules (fig. 1.17). Alternatively, in line with the procedure we will be using in the next chapter, one can define the plan as a septuple vertical split with ratios of 4:4:4:5:4:4:4 and a horizontal 11-way split with ratios, running from top to bottom, of 4:4:4:4:5:4:4:4:4:4:4. (In a true Palladian plan this type of description becomes a lot less clumsy.)

Barbaro had also said that houses should have the “symmetries,” meaning the modular structure, of temples. In fact Palladio’s Roman house really is that of a Vitruvian temple with six columns across the front, including a wider center intercolumniation, and eleven columns along the side. The only anomaly is the wider “column” just over halfway back. Thus does the domus romana indeed have the “symmetries” of the hexastyle temple described in Vitruvius 3.3.6. Indeed, the house plan could have been traced from the temple plan that Palladio drew to illustrate Vitruvius Let us note parenthetically that Palladio’s six canonical options for rectangular room-shapes, the 2:1\sqrt {2}:1, 1:1, 4:3, 3:2, 5:3, and 2:1, are identical to those Vitruvius gives for atria, peristyles, triclinia, and exedrae.

Palladio’s third view of the Roman house is half of the front elevation (fig. 1.18).41 This again buttresses Barbaro’s claim that the “symmetries” of the temple apply to the house. The elevation may not at first seem out of the ordinary—a typical Palladian facade with a colossal octastyle Corinthian portico flanked by plain, two-story, six-windowed wings.42 Yet the design proposes to illustrate Vitruvius’s Roman house with a type of facade that, at the very most, is rare in ancient Roman architecture. Most Roman houses, even the most luxurious, had little or no architectural ornament on the exterior walls, however gorgeous the interiors. Simple columned porticoes were fairly common. But the addition of the triangular pediment or fastigium, creating what looked like the front of a temple on the facade of a private house, was highly unusual, and indeed could be considered suspect and pretentious. Thus Cicero, in the most famous passage on the subject, denounces the presumptuousness of one of his enemies by saying: “this man would have [in his private house] a couch for statues of gods, a pediment, and a priest.”43 In the same vein Alberti inveighs against fastigia on private houses on the grounds that they subtract from the majesty proper to churches.44 Cicero’s and Alberti’s sentiments certainly go against Barbaro’s idea that houses should have the same decor as public buildings.45 But Barbara’s (and Palladio’s) powerful misreading of Vitruvius produced a type of house—a Palladian house rather than a domus romana, in fact—that has become so commonplace that we fail to see the novelty it possessed when it was introduced.46

1.18 Palladio’s Roman house facade. From Barbaro’s Vitruvius.

In short, the Renaissance development of the notion of symmetry—the thing itself if not its name—played a role in the elaboration of Renaissance domestic architecture. To review: beginning with Filarete, mirror symmetry across a vertical axis was considered desirable in a house. Francesco di Giorgio claimed that ancient houses had been similarly symmetrical. Cesare confirmed this and pretended to find a warrant for it in Vitruvius. Daniele Barbaro repeated his predecessors’ claims and added that a house should have the same beauty, order, and symmetries as a temple. Finally, Palladio himself illustrated the idea with a house whose plan actually seems to have been based on the plan of a Vitruvian temple, and which also had a temple front and colossal courtyard colonnade. By the end of this whole process, which occurred over a period of less than a century, the “Roman house” had been reinterpreted into something close to the Palladian villa.

But the way in which Renaissance domestic architecture developed its use of symmetry was in fact to differ considerably from Vitruvius’s rules for temples. Modules, grids, and the like played their role; canonical volumes were to be found; but the real laws involved the instinctive use of what we now recognize as reflective, bilateral, rotational, and glide symmetry. Our diagrams apply these modern concepts to the Renaissance forms. The first pure examples are Poggioreale and the Strozzi palace. Poggioreale, especially as revamped by Serlio, was a key element in the elaboration of central-plan symmetry, with later reflections in the work of Leonardo and in Palladio’s central-plan villas. As we shall see, it is in large part because it obeyed the laws of symmetry, in turn, that Palladio’s villa architecture lends itself so well to our type of analysis.

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