Hygiene and ritual in OMA’s domestic architecture


Between 1984 and 1998, OMA produced a series of small-scale domestic projects. Rem Koolhaas uses ces maison as a tool for reflection, allowing him to explore the ‘hedonistic dimension’ that characterises the architecture of the Modern Movement. Among the spaces that stand out in this lineage connecting the Dutch architect to the great masters, the bathroom is a particularly rich universe. In the work of Koolhaas, water is the central focus in the ongoing research intended to transcend strictly hygienic, functional considerations to define a genuine ritual choice of dimensions, perceptive relations, circulation paths and materials.


Abstract

Entre 1984 y 1998, OMA desarrolla una serie de proyectos de pequeña escala relacionados con el programa doméstico. Rem Koolhaas utiliza estas viviendas como útil de reflexión capaz de vehicular una exploración en torno a la “dimensión hedonista” propia de la arquitectura del movimiento moderno. Entre los espacios que destacan en este linaje que lo conecta con los grandes maestros, el cuarto de baño constituye un universo extremadamente rico. El agua se inscribe en el centro de un trabajo continuo que busca trascender la faceta estrictamente higienista y funcional para llegar a definir un verdadero ritual, al servicio del cual se deciden dimensiones, relaciones perceptivas, recorridos y materiales.


Casa Palestra, 1986

“In the recent attacks, modern architecture is always presented as lifeless, puritanical, empty and uninhabited. It has always been our intuition however, that modern architecture is in itself a hedonistic movement, that its severity, abstraction, and rigor are in fact plots to create the most provocative setting for the experiment that is modern life”.1

This paragraph opens OMA’s contribution to the exhibition Il Progetto Domestico. La casa dell’uomo: archetipi e prototipi at the 17th Milan Triennial in 1986. Curated by Marco Bellini in collaboration with George Teyssot, the exhibition featured a series of prestigious historians (Marco de Michelis, Robin Middleton, Monique Mosser and Anthony Vidler), who sought to reflect on the immediate future of the domestic space alongside thirty architects. Labelled ‘Casa Palestra’, Rem Koolhaas’s proposal was a rather provocative contribution to the debate, reviving a legendary project from the Modern Movement: Mies van der Rohe’s Barcelona Pavilion, which was dismantled at the end of the 1929 International Exposition. Not by chance, between 1983 and 1986, three professors from the Barcelona School of Architecture (ETSAB)2 embarked on a mission to build an identical reconstruction of the pavilion, triggering a heated controversy. Historian Francesco Moschini reveals the true nature of the Dutch architect’s installation: “OMA’s intervention at Casa Palestra is purely conceptual, expanding, profaning and treating as pure matter, as pure subterfuge, a sacred text for modern architecture: the Barcelona Pavilion by Mies van der Rohe” (1986,17).

The original project underwent a series of modifications with a twofold objective. On the one hand, to reveal the turbulent history surrounding the Pavilion’s dismantling through a mythological narrative of fictitious episodes created by Rem Koolhaas. On the other, to showcase the true ‘hedonistic’ dimension of modern architecture highlighted by OMA in the introduction to the project. The label ‘gymnasium house’ attached to Casa Palestra alludes to a series of scenes where professional actors (Fig. 1) appropriated this ‘sacred’ architecture and performed actions evoking those that took place in the changing rooms at the Downtown Athletic Club, an episode described in Delirious New York as an “incubator for adults” (Koolhaas 2004, 157). This attempt at demystification may be situated within the debate on postmodernism, but above all, it serves as a channel for experimentation that takes Mies’ work and his 1930s courtyard houses as a tool for reflecting on the act of dwelling, a topic explored in depth by the Dutch architect.

Figura 1.

OMA installation at the Milan Triennial. Source: OMA Archives.

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The conceptual framework underpinning this proposal turns Casa Palestra (1984-1985) into a true manifesto, a sort of highly radical playing field further developed in the Villa Linthorst project (labelled Patio Villa, 1984-1988), built later on in a low-density urban context. The disparity between the promise of the initial sketches and the final version points to the difficulties that arose during discussions with the client. Villa Dall’Ava was designed during the same period (1984-1991), but while the basic design was developed in an unusually short span of time, the four years that elapsed between the application for the building permit in 1985 and the execution project made in 1989 allowed Rem Koolhaas (1995a) to critically review and refine the final version.3 In the case of Villa Lemoine (1994-1998), the architect—now renowned both within and beyond the discipline—benefited from greater resources and full trust from the building’s future owner. These favourable conditions allowed him to salvage solutions and hypothesis that he had begun to work on in the past but that had fallen by the wayside. In an interview with Koolhaas’s former collaborator, Xaveer de Geyter, he stated:

[…] at that time, Rem was dedicating a lot of time to small-scale projects. […] Even when there were far more urgent things pending, he always took as long as he needed. Not only for this Villa, but also for the ones in Rotterdam and Bordeaux. He has always had a keen interest in minor domestic matters in detached houses.4

The ‘hedonistic’ dimension of the ‘gymnasium house’ is the driving force behind the project, giving rise to a series of architectural strategies used in the three ‘villas’: Linhorst, Dall’Ava and Lemoine.5 The relationship between water and the body, encompassing both hygiene and ritual, is crucial. This connection is explored through the iteration of a number of devices confined to the bathroom setting, a room that was extremely important for the Modern Movement, representing a lineage in which OMA is keen to position itself. In order to analyse the bathroom’s ritual dimension, Villa Dall’Ava is the most logical starting point as its central position will allow us to travel backwards and forwards in time. The photogenic rooftop swimming pool is a device whose contextual interactions occur at different scales, incorporating a mythological dimension rooted in OMA’s own history. While the pool’s position provides clear evidence of Koolhaas’s interest in the hedonistic dimension (Gargiani, 2004), its weight (both literal and figurative) overshadows other spaces that are intimately linked to water. More specifically, the master bathroom for Mr.and Mrs. Boudet, which adjoins the pool and has been overlooked in every analysis of the project.

The fact that the floor plans shown in S, M, L, XL (Fig. 2) do not include the final version6has largely contributed to this lack of interest. In order to remedy this oversight, Koolhaas sketched the executed layout next to the printed floor plan in red. The master bathroom’s apparent simplicity doesn’t reveal the underlying complexity deriving from the numerous reflections worked into the final version. The documents found in the OMA archives7 offer clear evidence of the amount of time spent designing this specific room, as well as the radical nature of the intermediary proposals. This article draws on three different sources: photos by Hans Werleman8 or by the author taken during several visits to the house, sketches from the OMA archive and a series of drawings produced by the author.9 This first axonometric projection will allow readers to understand the built version (Fig. 3). In order to more clearly display the different contextual relationships, the wall adjoining the swimming pool has been erased.

Figura 2.

First floor plan annotated by Rem Koolhaas. Source: S, M, L, XL (1995a).

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Figura 3.

Axonometric projection of the built project. Source: the author.

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In comparison with the large surface area devoted to Mr. and Mrs. Boudet’s apartment, the bathroom is not particularly spacious. Despite its dimensions, it stands out for the complexity of the spatial experience. This takes place across several perceptive levels and is enriched, enhanced and modulated by a combination of parameters: the careful positioning of the sanitary fittings, their relationship within a force field, and, above all, the finishes on the surfaces delimiting the bathroom, whose status varies according to three conditions lying on a spectrum between contrasting poles. The first transition is from opacity to transparency, with translucent elements playing a crucial role. The second transition is linked to movement, gravitating between fixed/static and mobile/unstable (hinged or sliding) devices. The third transition plays with varying degrees of reflection (light and image simultaneously), which range from matte white to concrete and mirrored surfaces. Although the perimeter of each area appears to be clearly defined when looking at the floor plan, these boundaries blur when the space is inhabited, offering several uninterrupted circulation paths with varying levels of permeability. The wooden floor covers almost the entire surface area, contributing to the programmatic and functional indeterminacy/instability. Borrowing strategies used by Le Corbusier on the ground floor of the Maisons Jaoul, material (dis)continuity constitutes a new parameter when it comes to managing uses and rituals.

Physical connections

The main spaces in the Villa are all linked in a continuous loop, taking full advantage of their dual status as a meeting place and as a connecting device to move through. Despite its usually intimate nature, the bathroom follows the same principle. It is a space for hygiene and ritual, but also for transition. It connects the terrace, the staircase leading up to the pool, the staircase leading down to the ground floor living room, the rest area and the work area. Its walls are subject to different kinds of movement: sliding, hinged, and pivoting. These dynamic surfaces structure the different circulation paths through three linking points which serve as both thresholds and connections. When moving upstairs from the living room, the open door cuts off the way to the bedroom on the left-hand side, rather like the door in Marcel Duchamp’s apartment in Rue Larrey, which gave access to the bedroom or the bathroom alternately. When the door is open, the south terrace can be accessed via the bathroom without entering the bedroom, whose passage remains blocked. When closed, it creates a circular pathway around the staircase linking all the spaces in the apartment. This strategy is picked up again in the Dutch House (1992-1995), a clear tribute to Mies. The parents’ apartment, located at the centre of the glazed prism, can only be accessed if the drawbridge covering the staircase is unfolded (Fig. 4). When raised, the inner sanctum is protected. Those on the outside can only skirt around it, unaware that a courtyard inside the room fills it with light.

Figura 4.

Cross section through the entrance to the parents’ apartment. Dutch Villa. Source: OMA Archives.

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At Villa Dall’Ava, a frosted panel nuances de presence of the backlit lavatory to the right of the landing. If we turn 180º, we realize we are already inside the bathroom. On the right, the wall adjoining the staircase is an immense mirror (Fig. 5). The black canvas in the background leads to the work area. The surface of the opposite wall is also clad in mirror, unfolding the space and multiplying the number of visual connections that contradict the physical connections (Fig. 6). This partition operates as a diaphragm, whose end transforms into a huge pivoting door that links the work area and the terrace. The two mobile planes (hinged and pivoting) are approached as fragments of a bigger canvas (Fig. 7). No hinges, handles or other elements reveal their status. In Koolhaas’s notes in S, M, L, XL (1995a), the first door is described as a “hinged wall” and the second as a “single pivoting plane” (184), negating their condition as ‘doors’ in both cases. Indeed, they are as thick as the rest of the partition (eight centimetres). When closed, the elements are all aligned on the same plane. On the side facing the bedroom, the absence of baseboards along its entire elevation gives it a different status from the other partitions.

Figura 5.

View of master bathroom. Hans Werleman. Source: OMA Archives.

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Figura 6.

View of master bathroom. Hans Werleman. Source: OMA Archives.

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Figura 7.

Axonometric projection of the built project. Source: the author.

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A frosted glass ‘column’ helps structure the promenade (Fig. 8). The absence of handles reinforces its abstract nature, while the surface akin to a sheer veil allows us to glimpse inside. Within this mise-en-scene, elements intended for hygiene play a central role, revealing the purpose of this space and the rituals taking place there: bottles, jars, and towels, almost levitating, alongside all the necessary installations (drainage of rainwater from the roof, ventilation and electricity). These elements come together in an ode to the flows needed to nurture and sustain the hygiene of the house and its inhabitants. On the ground floor, these elements are concealed within the concrete structure, while on the first floor, their importance is affirmed by their veiled presence. On the south terrace, the same strategy is adopted in the column placed against the side of the pool, where the drain, pump, filtering equipment, and forced ventilation system are all visible. While Madelon Vriesendorp’s drawing in Delirious New York (Koolhaas 2004, 234) showed the underground tunnels, ducts, and conduits beneath Manhattan that allowed an infinite grid to exist, in Villa Dall’Ava, these conduits are the very essence of the project.

Figura 8.

View of master bathroom. Hans Werleman. Source: OMA Archives.

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Visual connections

The nature of the aforementioned physical connections and spatial relationships is radically altered by the finishes. The different types of movement of the walls enable users to modulate a variable, proteiform gradient of privacy, where visual and physical connections sometimes overlap, intersect, contradict, or reinforce one another. Light comes to play a crucial role, with the contrast between exterior/interior and the interplay of natural/artificial light enriching these connections. The swimming pool features a unique contradiction that enhances its appeal. Despite being situated at the apex of the circulation path, both the pool and the access to it are completely invisible from the outside. The only staircase leading to the pool is concealed within Mr. and Mrs. Boudet’s box (Fig. 7). The sloping floor of the pool is not apparent from any of the façades. The only point of direct visual contact is on the first floor, in a private area only accessible to the couple themselves (figs. 3 and 7). As we walk up the staircase from the living room and open the door at the end, we move from the earthly realm of the garden, a suburban orchard bathed in sunlight, to the landing, which is dimly lit by the oculus (Fig. 9) and invites us to discover this aquatic world. Filtering through the water, a soft bluish glow reaches the inside of the staircase.

Figura 9.

View of swimming pool from the oculus. Hans Werleman. Source: OMA Archives.

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The dihedral obscuring the edges of the master bathroom is covered in mirrors, creating an authentic trompe-l’œil. The plane next to the staircase is set at an oblique angle, heightening the confusion further, as well as increasing the field of vision from the bathtub. When lying in the tub, one’s eyes wander beyond the bathroom area, reaching as far as the work area and back garden. Yet if we open the lateral frosted glass sliding doors a crack, the reflection allows us to look in the opposite direction, towards the south terrace, and further still, towards the huge window of the daughter’s apartment. In S, M, L, XL, Rem Koolhaas explains that “both panels slide to generate an open-air bath or shower” (1995a, 182). This direct visual connection may prove shocking, as a room associated with intimate rituals serves as a vantage point to observe and be observed, showcasing its hedonistic dimension. The bathtub has two headrests allowing one to lie at either end. Raised on clearly visible, lightweight feet rather than anchored to the floor, it appears to be movable—but to where? The answer can be found in two sketches from an intermediary version of the project. In the first (Fig. 10), the bathtub is a mobile element, intended to take advantage of the sunshine illuminating the south terrace. This ‘optimal’ orientation exposes the bathing ritual to prying eyes, giving rise to another form of exhibitionism despite being limited to the gaze of other family members.

Figura 10.

View from the south. Source: OMA Archives.

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The second drawing is an excerpt from the first floor plan of the version submitted for the building permit application (Fig. 11). The bathtub is an extension of the south terrace, blocking the physical connection with the work area but sitting in the middle of the visual axis, making it a centre of gravity for all the other spaces, which orbit around it. An axonometric reconstruction allows us to compare the consequences of this strategic position with those of the version that was ultimately built (Fig. 12). We believe that the set of mirrors in the final version is intended to restore this former centrality, doubling the exiguous space and situating the bathtub in the centre of a new, virtual setting. This approach was developed both before and after Villa Dall’Ava. At the Patio Villa, an intermediary version explores the possibilities of a bathroom, serving as both a space for ritual and a passage connecting the living room to the two bedrooms (Fig. 13). This option was abandoned in the final project, but frosted and mirrored surfaces in particular are once again present (Fig. 14). The introduction of the Patio Villa in S, M, L, XL opens with a photo of the main bathroom (Koolhaas 1995a). Next to it, the glossary lists the term “Bodies: […] Concentrating each night on just one area of his body allowed him to carry out the task of cleaning it and preserving it with greater thoroughness and attention to detail” (Koolhaas 1995a, 66).

Figura 11.

First floor plan. Version submitted in the May 1985 building permit application. Source: OMA Archives.

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Figura 12.

Axonometric projection of the preliminary project. Source: the author:

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Figura 13.

First floor plan. Preliminary project. Source: HNI Archives.

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Figura 14.

Patio Villa. View of master bathroom. Source: OMA Archives.

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Villa Lemoine exploits these forms of experimentation to the full (Fig. 15). To the left, there is an immense mirror-clad surface. Once again, a wet area functions both as a ritual room and as a passage between the independent quarters of Mr. Lemoine and those of Mrs. Lemoine. The bathtub, which appeared in the intermediary design for Villa Dall’Ava as an autonomous element that could be moved, reappears here in its built version. The bathtub’s mobility is obviously limited by the water supply and drainage points, but it is located in an ambiguous space belonging to the female realm yet visible from the shower (Fig. 16), which forms part of a masculine realm linked to the wheelchair. The two figures perform the same ritual, separated physically but connected visually in a game of seduction. Given the limited width of this bathroom-corridor, the glass panels dividing it from the courtyard function as mirrors, echoing a device already used by the architect at the Patio Villa. In this one (ahora hablo de la Patio Villa), Rem Koolhaas focused on different types of glass and their reflective properties, which varied depending on the viewer’s position and on the lighting conditions: “various kinds of glass comprise the south elevation of the house. Through translucent, clear, green-tinted and wire glass, the alternating effects of transparency, obscurity and reflection occur” (1998, 172).10 These effects are controlled and enhanced through two different kinds of surfaces, mirrored or glazed, whose capacity for reflection and transparency changes throughout the day.

Figura 15.

Villa Lemoine. View from master bathroom towards Mrs Lemoine’s quarters. Source: the author.

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Figura 16.

Villa Lemoine. View from master bathroom towards Mr Lemoine’s quarters. Source: the author.

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At Villa Dall’Ava, the narrow terrace maintains its dual status as a space for use and a space of communication with the daughter’s apartment (Fig. 17). The acid-etched glass surfaces that veil and sometimes conceive the bath and shower rituals operate on the same principle, both inside and outside the bathroom. The section that serves as an outdoor extension of the bathroom is dimly lit, turning the glass canvases into reflective surfaces that double the size of the façade opposite, echoing and bringing to life Le Corbusier’s well-known fenêtre-en-longueur. This sensation is heightened by the pivoting door to the right. On the partition between the bathroom and the work area, the mobile elements (hinged wall and pivoting plane) are painted glossy black. Under specific light conditions, these surfaces also reflect the surrounding space. Even the concrete in the shower becomes a reflective surface when it comes into contact with water.

Figura 17.

View of the terrace from Mr and Mrs Boudet’s apartment. Hans Werleman. Source: OMA Archives.

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Conclusion

At first glance, the wet areas in OMA’s domestic projects appear to be designed exclusively for the purposes of hygiene. However, a more in-depth analysis reveals that they were conceived as a means to explore and exploit the inherently hedonistic nature of Modern Movement space, as identified by Rem Koolhaas. The origins of this approach go back much further than the critical revisiting of the Barcelona Pavilion in the Casa Palestra alluded to here. The cells in the bathroom area in the 1972 project Exodus or The Voluntary Prisoners of Architecture “are equipped to encourage indulgence and to facilitate the realisation of fantasies and social inventions; they invite all forms of interaction and exchange” (Koolhaas, Zenghelis, Vriesendorp, 1977, 328). It is no coincidence that the images in the collage produced are taken from the feature film De Blanke Slavin (1969), written by Koolhaas with his childhood friend, Rene Daalder, a pioneer of Dutch sexual liberation cinema (Cfr. Lootsma 2001). The porthole of the swimming pool at Villa Dall’Ava articulates the relationship between ‘exhibitionist’ swimmers and ‘observer’ inhabitants. This strategy was already included in the 1976 project, evoked in The Story of the Pool, where the shared lobbies were situated at the ends (Fig. 18) and delimited by two glazed surfaces, through which “one saw the healthy, sometimes exciting underwater activities of the pool” (Koolhaas 1972, 356). Unlike the other proposals cited here, the members of the Boudet family swap roles interchangeably. They are at once active and passive subjects, bringing this hierarchy into play and creating programmatic, functional, structural, or urban instability, a quintessential Koolhaasian concept.

Figura 18.

Plan of swimming pool, published in Architectural Design. no. 5, 1977.

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This article reveals the complexity and intelligence of OMA’s work at every scale and shows how an entirely contemporary subject provides a basis for thorough architectural exploration, drawing on strategies and devices developed systematically in a series of trials repeated, adapted, and tested over a twenty-year period. These experiments encompass a wide range of tools and methods, including theoretical projects, manifestos and built works. At the same time, OMA aims to situate its work within a long line of twentieth-century dwellings11 that operate as both a benchmark and a source for introspection. In the case of the Barcelona Pavilion, this ‘genetic material’ from the past includes programmes that are completely unrelated in functional terms. By subverting and altering these vital works, the architect constructs a position embedded in the contemporary context. The relationship between water and the body goes beyond mere function to create a ritual space, where physical and visual connections intersect to offer an extremely rich perceptive and social experience. The tensions between the individual and the collective, public and private, intimate and playful serve as the drivers behind the project, creating ambiguous situations that evoke the complexities and constantly interchanging roles present in domestic life. This strategy has been transposed to large-scale projects such as the ZKM in Karlsruhe, the Centre for the Performing Arts in Miami, and the Casa da Música in Oporto. Contributing to this instability of hierarchies, the use and combination of different finishes takes on a new dimension that could be explored further in future research. Moving beyond the ‘collage’ dynamics often identified in critical analyses of OMA’s work, this article points to the need to study materials in terms of their capacity to modulate, modify, and intensify social and spatial relationships, creating powerful force fields capable of subverting an initial programmatic layout.

Bibliografía

1. 

AA. VV. 1998. OMA-Rem Koolhaas: Living Vivre Leben. Berlin: Birkäuser.

2. 

AA. VV. 2009. OMA. Villa Dall’Ava/Maison à Bordeaux. Tokyo: GA.

3. 

Chaslin, François. 2001. Deux conversations avec Rem Koolhaas et caetera. Paris: Sens & Tonka.

4. 

Fromonot, Françoise. 2014. “The house of Doctor Koolhaas”. AA Files, n.º 8:68-85.

5. 

Gargiani, Roberto. 2008. Rem Koolhaas/OMA: The Construction of Merveilles. Lausanne: EPFL Press.

6. 

Gargiani, Roberto. 2004. “Rem Koolhaas et le mythe de la Floating Swimming Pool“. Matières, no. 7 : 74-85

7. 

Lootsma, Bart. 1985. “The strategies of OMA”. Forum, n.º 3: 124-130

8. 

Lootsma, Bart. 2001. “Le film à l’envers: Les années 60 de Rem Koolhaas”. Le Visiteur, n.º 7: 90-111.

9. 

The Chicago Tapes. Transcript of the Conference at the University of Illinois at Chicago. New York: Rizzoli, 1987.

10. 

Koolhaas, Rem y Bruce Mau. 1995a. S, M, L, XL. New York: The Monacelli Press.

11. 

Koolhaas, Rem. 1995b. Entrevista en “Villa Dall’Ava”, filmado, escrito y dirigido por Richard Copans. Paris: Centre Pompidou.

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Koolhaas, Rem. 1998. OMA/Rem Koolhaas 1987-1998. Madrid: El Croquis.

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Koolhaas, Rem. 2004. Delirio de Nueva York. Barcelona: Gustavo Gili.

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Koolhaas, Rem, Elia Zenghelis, y Madelon Vriesendorp. 1977. “Exodus/1972”. Architectural Design, n.º 5: 328-329.

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Moneo, José Rafael. 2003. Inquietud teórica y estrategia proyectual en la obra de ocho arquitectos contemporáneos: James Stirling, Robert Venturi, Aldo Rossi, Peter Eisenman, Álvaro Siza, Frank Gehry, Rem Koolhaas, Herzog & De Meuron. Barcelona: Actar Publishers.

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Stellweg, Carl, Peter de Vette and Tara Lewis. 2019. Utopia Rotterdam 40 jaar. Rotterdam: Utopia

Notes

[1.] Introduction to the Casa Palestra project (17th Milan Triennial). OMA Archives. Koolhaas, Rem. 1986. All original texts have been translated by the author.

[2.] Ignasi de Solà-Morales, Cristian Cirici and Fernando Ramos.

[3.] “The long wait was bad in some ways, but good in allowing endless revision: it began as a beginner’s house: strident, colourful, etc.; it became a record of our own growing up.”

[4.] Interview with Xaveer de Geyter by the author. Brussels, August 14, 2019.

[5.] As a postscript to OMA’s work on the domestic programme, the exhibition Living / Vivre / Leben at the Centre d’Architecture Arc en Rêve (Bordeaux, February-May 1998) focuses on five small-scale projects, including the Nexus residential complex in Fukuoka.

[6.] The plans are from the building permit application (1985) and were intended to conceal subsequent modifications, which were eventually accepted as legal after four years of lawsuits.

[7.] The OMA archive is not digitalised. It is not usually open to researchers because it offers no working space and lacks sufficient resources. Its main purpose is to preserve the material produced for each competition and, in some cases, to lend specific documents to institutions for use in exhibitions.

[8.] Hans Werleman, cofounder and member of the Utopia collective. His friendship with Rem Koolhaas led him to become the main photographer of OMA’s early projects. The history of this self-funded arts organisation is published in Utopia, 40 Jaar (2019).

[9.] These drawings were produced using 3D modelling software as part of a research study carried out for the ‘Habilitation à Diriger des Recherches’, a certificate required to supervise doctoral research in France.

[10.] An almost identical description appears in the book S, M, L, XL (Koolhaas 1995a, 67).

[11.] ‘Farnsworth House (MvdR), Glass House (PJ), Villa Savoye (LC)’, cited in Koolhaas (1995b).