While the subject of formal analysis has often been studied, rarely has the distinction between form and content, and more importantly, between geometric form and topological form been articulated. The study of the diptych in both painting and architecture, which is essentially a relational (i.e. topological) and thus non-static, may do that.

When making abstract schemata of architecture, the numbers three and nine are traditionally used whether as a tripartite façade or a nine-square plan. Very rarely is a four-square plan or a two-part façade proposed, and when it is, it is as a two part opposition—solid / void, orthogonal gridded / round smooth. Such a binary opposition, which has underpinned thought in most disciplines, seems today to be insufficient or inadequate to deal with the complexities of the built environment in the post-mechanical age. In other disciplines in the humanities, foremost among them linguistics and philosophy, binary oppositions and paired relationships have come under an intense critique. The proposition contained below can be seen as adding another analytic frame to architecture, understood as a moving away from the existing analytic matrices.


The course will begin from a painterly idea of the diptych that originated as celebratory artifacts in Roman and Byzantine times, as wax and ivory grounds for inscription. Gradually the idea moved from a boxed horizontal surface to a framed vertical surface. This surface was suffused with both aspects of a diptych genre in its narrative and a structure in its formal manifestations. The second iteration of diptychs were usually religious themes, and in the case of Fra Angelico and Botticelli the theme of the Annunciation framed a formal opposition of light and dark, open and closed, inside and outside, mystical and real. As this opposition became sedimented through the centuries as a convention of painting, another element appeared to the binary opposition—the hinge—which returned the diptych to its physical origins in Roman times. Moving forward to today, a hinge in architecture, like the separatrix in language, is both a concept and necessarily a physical act. According to Jacques Derrida, the hinge makes the impossibility that a sign, the unity of a signified and a signifier, can be produced within the plentitude of a present and an absolute presence. The hinge is a break that joins; it is absolute difference. To re-conceptualize the idea of a binary opposition as a hinged diptych is to swerve from existing analytic matrices to produce a more expanded view of such binary relationships. That is to distinguish between mere juxtaposition or binary oppositions, such as binuclear relationships that are already present in architecture. The object of the class is to ultimately produce a new matrix of solutions that deal with the possibility of partial as opposed to fragmentary figures, and simultaneously deny the political power of symmetrical frontal imagery inherent in triadic relationships.


Initially, the students will research work from the history of painting and architecture to make a catalogue of potential models. These will be broken down into a typology of three categories: content narrative, geometric structure, and topological structure. The last half of the semester will be spent using these categories to produce analogous architectural examples, until there is a matrix of necessary conditions that will define the diptych today in architecture.

Date Topic
09 January 1. Diptych – Introduction
16 January No class/Monday classes meet
23 January 2. Geometric Analysis of Paintings
30 January 3. Geometric Analysis of Paintings
06 February 4. Topological Analysis of Paintings
13 February 5. Topological Analysis of Paintings
20 February 6. Geometric Analysis of Architecture
27 February 7. Geometric Analysis of Architecture
6 March 8. Topological Analysis of Architecture
27 March 9. Topological Analysis of Architecture
3 April 10. Development of Elements
10 April 11. Development of Topological Relationships
17 April 12. Development of Topological Relationships
24 April 13. Final Presentation of Analyses and Synthetic Typology

All Semesters

Spring 2017
Diagrammatic Analysis: The Space of Time, Part I—Lateness
Peter Eisenman, Elisa Iturbe
Spring 2016
Diagrammatic Analysis
Peter Eisenman