Interior space of the Rotunda di San Tomé. The neat overall tectonic order grows out of happenstance stereotomy.
Introduction
Upon entering on a bright summer day, it takes a couple of seconds to get used to the dim lighting of the Rotonda di San Tomé and absorb the straightforward tectonic order of this 12th-century marvel of Lombard Romanesque architecture.[1] The central domical space is defined by the pyramidal stacking of an ambulatory and a gallery. The building is enclosed by massive, stone walls, with eight columns arranged concentrically on each level in the interior. Upon closer inspection, it becomes apparent that this neat overall tectonic order grows out of total disorder: Each column is different, some capitals are inverted column bases from earlier building phases, the stereotomy of the arches is distinct in each bay, the layers of the stone masonry both in the dome and the wall are uneven [ 1 ].
Fast-forwarding eight hundred years, another dome of comparable dimensions was erected in Jena, Germany, for a temporary planetarium. It was the world’s first geodesic dome, and a pioneering thin concrete shell (the grid was sprayed with concrete).[2] The steel grid was designed with a precision of 1/20 mm, which is beyond even the current state of the art in metal-working capabilities. Only thirty years later, a late descendant of the Jena planetarium dome —a clever, yet unassuming, thin concrete shell factory roofing in Hungary —got extended.[3] The project marked one of the early uses of computers in design. The extension mimicked the original geometry, but it was based on a more intricate mechanical model, not manageable by hand calculations. The complexity of those calculations stems from the slight modification of the original geometry. Ever so subtle, that it is hardly noticeable; moreover, it barely affects construction.
The builders of all three examples erred in their treatment of precision, as in, alignment: San Tomé is less precise in its details than one would anticipate, while the two shells aim at more precision than what is physically feasible or what is noticeable. Such errors result in inconsistency between design, construction, and perception. However, once we consider precision in the metaphysical sense, as in matching the intent, they all seem to be just precise enough. The paper identifies this conflict between precision in the metaphysical (idea) and the physical (materialization) sense as one way to create poetics in construction. Precision, in its metaphysical sense strongly influences the narrative of the building, which in turn impacts affect.
This paper is not about the vanity of precision. It is also not a swansong for the ancient unity of material, building, and construction in the age of codified design and computers. Rather, it is about the (correct) scale and zoomability of tectonics in a digital era.[4]. I will use Frampton’s definition as a starting point, which states that tectonics is “structural and material probity but also a poetics of construction”.[5] Such a definition is well-positioned to consider when and which tools and measures are appropriate in design and construction, so that they enable rather than control the process, and hence, ultimately, serve both probity and poetics.
This paper is, furthermore, about being fallible as a builder (that is, being inconsistent as designer and/or constructor). If being fallible, or to err, is essentially human, is that desirable, necessary, or permitted within the realm of architecture today? It is beyond the scope of this paper to lament whether the future of architecture, including program and tectonics, is to be defined by humans or machines. However, I attempt to show that architecture becomes poetic precisely because of the minor inconsistencies, errors, that create a rift between what it is meant to be and how it materializes, i.e., between the act of construing and the act of constructing.[6]
The selected examples are fraudulent in many ways: they all represent the same, special architectural form (domical space), were not conceived by an architect, and are all conveniently dated. However, they share two features that make them well-positioned to illustrate the arguments of this text: They all treat structural and material probity as commonplace, which makes them highly tectonic, and they are all extremely functional or programmatic.[7] Their similarity to each other and their good match with many qualities appreciated in tectonic architecture make them excellent guinea pigs to test the hypotheses of the paper: First, that precision is a design parameter that is dependent not only on the tools and materials but also on intent. While this might seem obvious, it is easily overlooked when our current tools allow practically infinite precision. Second, that subtle inconsistencies between idea and materialization can be virtues, and more importantly, they might be the features that create affect, or poetics. Consistency between design and construction (i.e., focusing on probity) was rightfully pursued when architecture was, by default, created by humans, who are inconsistent by nature. In an era, however, when machines, being presumably consistent by nature, are becoming increasingly involved in the generation of architecture (including design and construction), to preserve poetics, maybe it is the desired level of consistency that deserves a closer look.
Dramatis Personae
As the three buildings used as case studies throughout this paper are not widely known, a short introduction seems adequate.
The Rotonda di San Tomé, also known as San Tommaso, is located near the town of Almenno San Bartolomeo, outside Bergamo, Italy. It was built in the 12th century, likely replacing an earlier structure and reusing some of its building materials. It is a well-preserved edifice of Lombard Romanesque architecture, characterized by its distinctive features, including a sparsely decorated exterior (lacking sculptures) and a series of blind arches crowning the walls, divided by pilaster strips. The circular building with a 16‑m diameter (exterior) was constructed using local stones, without mortar, and featured 1.15 m‑thick walls filled with rubble. The few openings are strategically placed, elevating lighting into the transcendent. While its origins are debated, it is assumed that it was part of a female monastery from the 13th century; as such, it served both the local community and the convent. This dual purpose is evident in the distinct narratives and different craftsmanship of the ambulatory and gallery detailing. The latter, which served the nuns, is more refined and nuanced. The central space is capped by a stone masonry dome with an oculus on top and four openings (two in the shape of a Greek cross and two circular) arranged evenly around the base. The structure repeatedly sustained severe damage over the centuries, due to lightning, and it has been restored multiple times.
First Planetarium of Jena, exterior. The geodesic grid is recognizable under the thin layer of concrete.
The so-called first Planetarium of Jena, built in 1922, was a temporary mockup structure erected on the top of a building in the Zeiss Factory [ 2 ]. Zeiss, a manufacturer of optical devices, developed a new planetarium device and needed a smooth, spherical surface to test it. The dome was designed by Walther Bauersfeld, the lead engineer of the planetarium device. Due to the temporary nature and limited load-bearing capacity of the roof, he opted for a lightweight solution. The original design of the 16 m‑diameter dome envisioned a light steel grid dressed in canvas. However, canvas was not available at the time, and Bauersfeld, advised by the concrete-contractor Dywidag company, decided to spray the grid with 3 cm of concrete. Hence, this dome became the unlikely early prototype of the pioneering Zeiss-Dywidag reinforced concrete shell construction system. While the reinforcement in an ordinary reinforced concrete structure is also assembled before the concrete is poured, it is usually done over formwork. Bauersfeld’s grid was self-bearing. It was a triangulated grid, created as the subdivision of a spherical icosahedron, made of approximately 4,000 pieces of 60 cm long steel bars. As such, it was a geodesic grid, built more than 20 years before Buckminster Fuller coined the term ‘geodesic dome’. Bauersfeld lacked the means (in terms of theory and computational power) to calculate such a complex structure as a space truss; instead, he devised an ingenious rule for triangulation that allowed him to estimate the strength of the structure as a continuous surface. It also allowed him to use relatively few different bars, all within 20% difference in length. Intriguingly, he settled for a “reasonable” approximation of what he aimed for (equal-area triangulation of the sphere), and yet he prescribed the length of each bar with 1/20 mm precision (that is less then 0,01%).
KÖFÉM Factory, second phase, shell roofing. The design accentuates the uninterrupted horizontal joint between wall and roof, despite the segmented shell roofing.
The roofing of KÖFÉM Factory is a cast-in-place thin concrete shell, designed by Lajos Kollár, a structural engineer and internationally established scholar of shell structures. The building is an eminent example of mid-twentieth-century industrial modernism in Eastern Europe, where shell structures enjoyed a late heyday (compared to Western Europe). As labor was cheap, their material efficiency made them an economic choice, a prime argument in the centralized, socialist building industry. It was built in 1967 as an extension of an aluminum processing plant in Székesfehérvár, Hungary. The roofing consists of a series of saddle shells (30 m x 11 m span, with a thickness of 6 cm). The first phase (completed ten years prior, and visually identical to the second phase) spearheaded a renewed interest in cast-in-place concrete shells in Hungary after WWII. It was much celebrated for its economy and simple, but elegant shape.[8] While saddle surfaces are both practical (it is easy to integrate clerestory windows) and structurally beneficial, their joint with the enclosing walls creates a design challenge (the edge of a saddle is curved by default). The original KÖFÉM design addressed this issue by adding a conoid segment to the shorter edge of the saddle, enabling a continuous, horizontal joint with the wall [ 3 ]. Kollár’s main contribution in the second phase was that he substituted the three shell segments (two conoids on the side and a saddle in the middle) with a single, continuous surface, i.e., he ‘form-found’ a shell with two curved and two straight edges. He achieved a geometrically more honest solution, but it required a different, more complex mechanical model, hence, more complex calculations.[9]
Observing chronologically, there is a move from assembly towards continuum, from rugged to smooth. The two later structures also challenge the Semperian categories of stereotomic and tectonic (i.e., frame-like), eventually dissolving into a hybrid form. It is hence tempting to simplify the emerging story on precision into a trend from lesser to greater. This simplification would miss the point, as it only considers precision as a physical phenomenon. Metaphysically, precision emerges (or should emerge) as a balance between materials, tools, and processes. In short, it is intrinsically linked to the context. In this sense, all three buildings are extremely precise, and it should strangely be most evident for San Tomé, which is the ruggedest of them all: Just imagine what it would take today to erect a building of comparable dimensions as dry (!) construction (no mortar, no binder).
Metaphysically, as I argued, precision is also linked to intent, which creates a non-tangible layer of tectonics. As I will show, the subtle primacy of idea over materialization is apparent in all three cases. All builders erred, ever so slightly, on the side of the idea, and this translates into tangible inconsistencies in precision in the physical sense.
Dome, Rotunda di San Tomé, showing the clerestory openings
Narratives and Perceptions
While the Rotunda has a central layout, it has an orientation: the altar, the focal point in the Christian liturgy, is placed in an apse towards the north-eastern side. This disposition slightly deviates from the traditional east-west orientation of Christian churches, for a good reason: It has been shown that the axis aligns with that of the rising sun on July 3rd, which celebrates the translation of Saint Thomas, to whom the Rotunda is dedicated.[10] Lighting plays a crucial role in the symbolism of the Roman liturgical space. Accordingly, the perpendicular axes created by the clerestory openings on the drum follow the same orientation, allowing the rising sun around the summer solstice to project the Greek cross into the Rotunda. During the winter solstice, the cross appears with the setting sun. This careful overall composition, with the nuanced orientation and shaping of the clerestory windows, is in stark contrast (or, inconsistent) with the ‘happenstance’ stereotomy of the building, which Kingsley describes as “(…) formed of rather roughly dressed blocks showing great variation in size.”[11] [ 4 ] . While such roughness is most likely related to the incorporation of reused material, and as such, obeys or embraces an external constraint, there is also an intent. There is an apparent preference for alignment with the ethereal by incorporating cosmogonical symbolism, as opposed to alignment in the banal sense, as in obeying the horizontal when laying courses. In terms of precision, as in alignment, the Rotunda is not necessarily a story of what was possible, but about deliberate choice, which results in inconsistent tectonics.
Inconsistency is also encoded into the tectonic narrative more explicitly: as briefly mentioned during the introduction of the buildings, there are marked differences in craftsmanship, material, and, though less relevant to the present discussion, in ornament, between the two stories of the interior spaces. Historians link those differences to the use of the space.[12] They argue that the ground floor is finished in a much cruder manner than the gallery, as per the client’s preference. The ground floor was intended for the populus, while the gallery served the community of the convent. Accordingly, their construction is credited to two different groups of masons, with those working on the gallery identified as having more advanced skills. The use of pilfered material is most apparent on the ground floor: the columns are reused from (likely) an earlier building phase. As they did not meet the height requirement for their new placement, they have been accommodated by various measures. This variety is linked to the different dimensions of the pilfered bases (many of them former capitals). The capitals across the eight columns have varying heights and differ in shape and ornament. In contrast, the columns in the gallery appear to be custom-made for the Rotunda. Their formal language is consistent, with all capitals based on the Corinthian style – albeit their ornament is also unique. Having unique ornamentation for each capital was not uncommon in Christian religious architecture, as the sculpted elements were literally meant to tell stories, in this case that of Tobit from the Old Testament.
These differences in the tectonics of the two ambulatory spaces can also be understood as differences in precision (as in joining, richness of detail, or smoothness). Based on what we know, this also appears to be a deliberate act. The emerging overall tectonics is not a mere consequence of the use of reclaimed material or a certain level of craftsmanship. It is guided by a programmatic intent; hence, the narrative is carefully construed.
In case of San Tomé, even without the historical details and my interpretation, much of its tectonics is relatable, ‘readable’, the act of construing can be physically experienced. This also holds, though to a lesser extent, for elements that are intangible, such as the message of the lighting. However, construing can remain unseen for the most part, as is the case for the two other domes discussed below. Just like with a text, the ‘readability’ of architecture is not, and has never been[13] absolute; it depends both on the creator and the reader (user).
Construing and Constructing
Frascari refers to tectonics as both constructing and construing.[14] Constructing encompasses a whole range of activities from conceptualization to materialization, from material engineering to the joining of steel bars that eventually lead to a construct. Much of the theory of construing, implicitly or explicitly, is related to the idea(l) of a thinking hand, an intuitive (and human) understanding of the innate properties of material and the process of construction.[15] Per the premise of this paper, I suggest that an intuitive understanding of both tangible (as material) and intangible (as geometry and structural behavior) aspects of the act of building can manifest as construing. An intuitive understanding (expertise) is developed over time through dedication. A preference for using that intuitive knowledge is the payoff for such a cognitively costly process. It creates a subjective (or biased) focus during the process.[16] I argue that this focus inadvertently creates minor inconsistencies in tectonics, which can affect (and possibly benefit) its perception, and often manifests itself in relation to precision.
Original Zeiss planetarium projecting device
Subdivision scheme, geodesic gridshell of the first Planetarium of Jena.
Bauersfeld, who designed the geodesic gridshell encased in concrete for the Zeiss Planetarium, was a mechanical engineer by training and worked in the optical industry. He developed the concept for the modern planetarium projecting device [ 5 ], for which the dome was to serve as a testing ground. When prompted to design a matching, domical projecting surface, he turned to the same Platonic solid, the icosahedron, which served as a base for the design of the planetarium device. Because the structure had to be lightweight, he considered a gridshell. The requirement for smoothness necessitated the subdivision of the icosahedron’s faces. He developed a specific subdivision scheme, based on the spherical projection of the icosahedron, which resulted in an almost equal-area triangulation[17] of the sphere [ 6 ].[18] Bauersfeld’s expressed motivation in pursuing an equal-area triangulation was to ensure a good fit between what he intended to build and the structural model he wanted to use. He aimed to approximate the dense assembly of the bars as a continuous shell surface, and the chosen tessellation provided a reasonably uniform distribution of bars.
By opting for a gridshell, Bauersfeld chose a structural solution that was materially and economically feasible, like any engineer would. There is no clear rationale for connecting the geometry of the gridshell to that of the projecting device, though. As the final surface was meant to be plastered/concreted over, its tangible impact was much limited. Such geometrical finesse was a subjective preference, a poetic component of construing, and yet, not completely l’art pour l’art. Construction and perception also benefited from Bauersfeld’s deep, intuitive understanding of the geodesic geometry (i.e., a geometry based on a spherical polyhedron). There is an intricate balance of how a geodesic geometry is perceived (how smooth a tessellation looks) and how complicated its assembly is (how many different bars are needed), and Bauersfeld’s solution provided an excellent trade-off.[19]
There is an interesting fluctuation of idealism and pragmatism in Bauersfeld’s work that affects both construing and constructing. During the design phase, when he aimed at the equal-area tessellation he was an idealist, when he settled for the approximating algorithm, which also allowed him to standardize much of the bar-lengths, he was a pragmatic. And yet again, in the phase of construction, once the bars needed to be dimensioned, he prescribed their lengths within 1/20 mm precision, neglecting the realities of steel construction. There is an anecdote, however, shared by a long-time collaborator of Bauersfeld’s, Franz Dischinger, on a subsequent project, where a bar that was off by only 1 mm (on a 60 cm length) caused such deformations in the grid that construction had to be stopped and the faulty bar replaced.[20] Prescribing precision an order of a magnitude higher than the permissible range of error makes sense. Rather than seeing a fluctuation, the process can therefor also be interpreted as guided by intent[21]. Being loose where possible and strict where necessary. Moreover, the recursive formula he used for the triangulation of the sphere, instead of being a generator of imprecision (even if very small), can be understood as a simultaneous act of construing and construction[22]: It works as if someone were drawing or acting out the subdivision. It can be understood as a metaphysical link between tools and processes.
Bauersfeld’s brilliance was in his ability to overcome the limitations of his tools (i.e., pen and paper) during the complex optimization task he undertook. His approach was theory-driven. Lajos Kollár, the designer of the KÖFÉM extension, on the other hand, leveraged the then-emerging technology of computers to tackle a problem that was previously successfully approximated by hand calculations. His approach was driven by technology, but, like theory did for Bauersfeld, technology served Kollár’s vision.
Kollár was at the same time a practicing structural engineer with extensive experience and a respected scholar and academic. He felt that engineering education lacked strategies to develop design thinking, and he emerged as an advocate for a holistic approach to design, something he actively pursued in his practice. In the case of the KÖFÉM factory, the poetic he sought was an honest match between geometry, structural behavior, and perceived forms.
Enablers and Controllers
The three examples —San Tomé, the Planetarium, and the KÖFÉM roofing —suggest a trend from less to greater control during the design phase, and consequently, less autonomy for the builders. Indeed, such a trend exists. The engineering revolution in the eighteenth century altered our expectations of design: we require more certainty, which is generally a good thing, as it leads to safer construction. We are, nevertheless, obliged to question the desired level of control case by case, so that it enables high precision, in the metaphysical sense, achieving the desired trade-off between materials, tools, and processes.
Shells are extremely thin structures. They can be thin, because (thanks to their curved shape) they primarily carry their loads through compression and tension which is more effective than through bending. Their thinness makes them highly impactful as tectonic objects, but it also makes them highly susceptible to mistakes, including those during design and construction. Therefore, while the theory of shells developed rapidly in the first half of the twentieth century, model building and testing, often on a full-scale basis, remained an integral part of shell design. The collapse of the mockup built to demonstrate the feasibility of the original design for the KÖFÉM factory roofing (first phase) almost sank the project. Eventually, the design could proceed, as the investigation identified that construction deficiencies caused the collapse. Such dramatic events, as the collapse of the mockup, were rare. Instead, the model experiments helped designers and contractors evaluate their predictions based on theory alone and refine their structural models accordingly. Kollár had extensive experience with physical models, which gave him an intuitive, experiential understanding of the behavior of shells and an appreciation for the more complex, computationally intensive structural models for shells.
Shell surface of the KÖFÉM Factory roofing
The so-called membrane model, which completely disregards bending moments in the shell, is elegant and straightforward, but its applicability is strictly constrained. While it suits certain processes well (such as form-finding), in other situations, it becomes a controlling rather than an enabling tool. Such limiting control affects tectonics. As described in the introduction to the buildings, the first phase of the KÖFÉM Factory roofing appears to be a continuous shell from wall to wall, but in fact, it consists of three shell segments. Moreover, technically only one of them, the saddle in the middle, acts as a shell; the conoids are cantilevered from the walls, and their behavior is closer to a plate. The first phase design, from an engineering point of view, was ingenious: the saddle’s shape (side-length ratios) was chosen so as not to exert any thrust on the conoids [ 7 ]. The design creatively relied on the simpler membrane model to minimize calculations (which were done by hand), but a dissonance remains between perception and behavior. Kollár resolved that dissonance by defining a single, continuous surface that acted as a shell, albeit one that’s behavior is more complex[23] than what the membrane model can describe. The then-emerging computers enabled him to apply the more complex model accordingly, and, from a conceptual point of view, to pursue a more holistic aim.
The consistency Kollár achieved in the second phase of the KÖFÉM Factory is exciting from the perspective of this paper, as it is almost post-human, which would make him the opposite of fallible. However, it is essential to note that his design builds upon an existing one. He did not change the material or the construction technology. The two geometries are indistinguishable to the untrained eye (most eyes are untrained). He changed an excellent design mainly to make the unseen, right. Not unlike Bauersfeld’s dimensioning, his process seems too precise, in the physical sense.
Epilogue
As exemplified above, high precision in the physical sense can be both a virtue and a vice, and it can be interpreted vastly differently depending on the materials, tools, and processes involved. Today, amidst rapid technological development, it is tempting to opt for higher precision, because the construct is made infinitely zoomable during the design phase. The then-emerging tectonics is only construed, though, it is virtual. To allow for construction to shape tectonics in the physical realm, it is vital to treat precision in the metaphysical sense, which depends on the context and not on scale.
The discussed case studies represent different regions on the broad spectrum of architecture, spanning from the primordial hut to structural art. In the physical sense, their precision is in vastly different dimensions, metaphysically however, all three are just precise enough. They are all highly programmatic; they show honestly what they are made of and how they stand up, and, while for different reasons, each of them is poetic. I argue that they are poetic because they err in their treatment of precision, in the physical sense. They treat it inconsistently. Such inconsistency is present in each case either within the design concept or it creates a rift between the idea and its realization.
These examples are shaped by these subtle inconsistencies, because their creator was fallible. The tangible precision of each project is not only subject to what was possible, but to what the designer intended. Those intents are highly subjective, informed by a dedication (to the divine), or years of training in theory or practice. To fall for one’s interest or intuition, to be biased, to err in this sense, is in fact, no longer only a human trait. Just as architecture is no longer practiced by humans without significant assistance from technology. It is therefore vital to be mindful of the role inconsistencies played in creating the various components of tectonics in the past. It might guide us in shaping architecture to our liking in the future, either consistently or inconsistently, but intentionally.