04 Crystals and Symmetry

Andrea Palladio, Villa Capra. Vicenza, Italy, 1566

Where does form come from? What are the underlying elements and processes that govern the formation and shapes of organic and inorganic objects? What role does symmetry play in creating and understanding them? Addressing these questions—all of which revolve around the relationship between invisible interior structures and exterior shapes—is a cultural task that is often assigned to scientists and philosophers. However, the same issues have long been of interest to architects and architectural historians. During the 19th century these questions and these disciplines often overlapped with one another. Symmetry was particularly important in establishing the relationship between the internal organization and the external appearance of crystals. And crystals and symmetry held an important place in architectural history and design.

Crystal Structures

Plato believed that the basic units of the cosmos were the five-regular polyhedron: the tetrahedron, the cube, the octahedron, the icosahedron, and the dodecahedron. These elegant elements, each composed of identical planes symmetrically arranged at equal angles, were thought to be the building blocks from which the universe was constructed. The importance of these symmetrical figures held sway in the scientific theories of Johannes Kepler and Robert Hooke in the 17th century. Their respective investigations of macro and microcosms relied on the heuristic power of their predictable geometry.

In Hooke’s 1665 Micrographia, he theorized that the internal organization of crystals conformed to the angles present in Plato’s polyhedra (30, 60, 90, 120, 180). He held that the specific forms that crystals took adhered to the geometry produced by the periodic packing of spheres. Four years later the Danish scientist Nicolas Steno would reveal the limits of the Platonic geometries. Based on accurate measurements of literal crystals, he agreed with Hooke that the angle between their faces was always consistent. However, the angle that described that relationship did not always adhere to the five found in the Platonic solids. Steno’s advances were aided by applying the descriptive techniques of measuring and making polyhedra using templates of tessellated planes developed by the German artist Albrecht Dürer in the 16th century.1

Soon after the turn of the 18th century, and after Legendre’s redefined notion of symmetry was published in 1794, crystallographer René Just Haüy “was able to formulate the law relating the measured angles of crystal forms to an internal repetition of identical molecules” inside of them. From this hypothesis he was able to begin to establish the symmetrical internal molecular structure of all natural elements.2 Empirical analysis showed, and in 1840 Johann Hessel proved, that there were only thirty-two symmetrical combinations of molecules in crystals. In 1848 Auguste Bravais established that there were only fourteen different orientations or symmetrical lattices in which these molecules could be arranged. Finally, in 1891 Evgraf Fedorov and Arthur Schoenflies found that there are only 230 symmetrical configurations in which the internal molecular structure of a crystal could be arranged.3 Thus, despite the myriad of external forms, the internal logic of minerals was discovered to remain always symmetrical. In other words, symmetry was always present in the world, even when our senses could not detect it. If it was the job of scientists to establish these facts in the 19th century, then it was the task of artists to translate this information into recognizable cultural codes.

Reflections

As both a model and a metaphor, crystals were central figures in 19th and early 20th century art and architectural history. As in crystallography, the goal of many artists and historians was to establish a clear relationship between the external appearances and the invisible structures that governed the creation of material and cultural artifacts. One artistic genre in which the affinity between natural and artistic forms was found especially productive was architectural ornament.4 Prominent art historians, such as Alois Riegel, Wilhelm Worringer, and Aby Warburg, saw in the symmetries found in traditional ornament a link between crystal formation and artistic form.5

In architecture, literal references to crystals were also used to produce new forms. As a process with a consistent internal structure that could produce asymmetric forms, it was an ideal analogy for those wishing form to be both guided by rules and free from their prescribed results. In the early 20th century crystals were associated with mystical and utopian projects, such as Bruno Taut’s Alpine Architecture. 6 In the latter half of the century they were used in a more literal fashion by architects like Zvi Hecker and Alfred Neumann.7

Perhaps the subtlest and most unexpected translation of the inner symmetries of crystals into architectural form is found in the work of Frank Lloyd Wright. Throughout his career local and global symmetries lurk underneath the dynamic massing and spatial arrangements of the body. These hidden symmetries had their source in both crystallography and in traditional ornaments.

It is well documented that, as a child, Wright played with the so-called Froebel “gifts.”8 Less well-known is the fact that, before he became a childhood education theorist, Friedrich Froebel was a crystallographer in the early 1800s. The fact that the components of Froebel’s toys were all symmetrical, as were the operations he prescribed for manipulating them, had its origin in the structure of crystals. His goal was that, by physically rotating, reflecting, and translating these materials, a child would learn the underlying logic of the physical world. However, this knowledge did not come from controlled experiments within language or mathematics, but via direct experience with the body.9 When Wright claimed that he could “still feel the blocks in his fingers” eighty years after playing with Froebel’s blocks, he was not just recalling his childhood, but unknowingly mimicking the underlying symmetries found in the material world.

Wright’s work does not look crystalline though. But a review of it, especially of his plans, reveals the multiple reflections, rotations, and glide-reflections at work. They are the same operations prescribed in Froebel’s system, and the same ones found in the thirty-two nets and fourteen lattices that describe crystalline structures. They are also the operations found in traditional architectural ornament. Wright learned the logic of ornament in a similar way by which he learned about three-dimensional form from Froebel: not abstractly, but physically. He told the story of his tracing every line in his uncle’s copy of Owen Jones’ book The Grammar of Ornament, a book that documents symmetrical ornamental motifs from around the globe.

The site plan of the Darwin D. Martin House in Buffalo (1905) reveals a series of local rotational symmetries across the property, while the plan of the main house reveals reflective symmetries in each of the main social spaces, as well as a global reflection that organizes the library, the dining room, the living room and the porch. However, as with crystals, its asymmetrical external appearance and its internal spatial configuration mask these underlying operations. Likewise, his early suburban planning schemes, such as the Quadruple Block Plan (1901), subject an asymmetrical house to a series of reflections to produce a symmetrical effect. Similar results are seen in his unofficial entry to the Chicago City Club Housing Competition (1916) for an urban subdivision. In fact, the larger the scale that Wright worked at—like the Crystal City outside of Washington, D.C. (1940)—the more symmetries one finds.

His plan for the Unity Temple in Oak Park, IL (1908) shows a clear globally reflective organization. However, one rarely sees or experiences the project in this way. In the interior, the visitor is always taken off the central axis, and the still symmetrical translational and rotational effects are made more visually prominent. The tension between the two tall, centrally organized masses and the overall horizontal and asymmetrical effect reinforces the co-presence of symmetry and asymmetry: while symmetry is persistently present at the level of organization, it is not at the level of perception.

A common motif in the Froebel system is the rotationally symmetric pin-wheel. This can be found in many of Wright’s skyscraper schemes, such as St. Mark’s in the Bouwerie (1931) and the Price Tower (1956). The Guggenheim Museum (1959) also conforms to a rotational logic. The spiral is a common crystalline structure, achieved by a consistent rotational movement in the x-axis and a translation in the y-axis. Across Wright’s diverse sensibilities and appearances—the long and low Prairie houses, the pin-wheeled towers, the massive Unity Temple and Guggenheim—what remains consistent is the underlying symmetrical operations— just as one finds in crystals.

Translating Symmetry

It is significant that Frank Lloyd Wright’s symmetries mostly occur in plan. The plan is to architecture what the diagram is to science, or what the equation is to math. It is not something one encounters in the world. Rather, it is the thing that encapsulates ideas while abstractly organizing spaces, activities, movements, and perceptions. Like the symmetrical nets and laws governing the form of crystals, the plan invisibly manages forms and behaviors. In chemistry, knowing how matter was organized enabled it to be manipulated in novel ways. The results of these operations are what we call chemicals. In architecture, Wright’s mastery of symmetry (and steel and concrete) allowed him to create a new architectural idiom, what he called “nature patterns” or “integral ornament,” both dependent on the understanding of the “nature of materials.”

“And when I say Nature, I mean inherent structure seen always by the architect as a matter of complete design. It is in itself, always, nature-pattern.”10

“(…) Integral ornament is the developed sense of the building as a whole, of the manifest abstract pattern of structure itself (...) Integral ornament is simply structurepattern made visibly articulate and seen in the building (…) It is the expression of inner rhythm of Form.”11

Where does form come from? In the case of Wright, it comes from a variety of cultural contexts, but also from the inner workings of crystals, from architectural ornament, and from their common symmetrical structures.

1 Cecil J. Schneer, “The Renaissance Background to Crystallography: The Search for Harmonious Proportions and Perfect Shapes in the Natural World Opened the Way to the Science of Crystals,” American Scientist vol. 71, no 3 (1983) 254-263. 2 Ibid. 262-263. 3 A.V. Shubnikov and V.A. Koptsik, Symmetry in Science and Art, edited by David Harker (New York: Plenum Press, 1974). 4 Barry Bergdoll, “Of Crystals, Cells, and Strata: Natural History and Debates on the Form of a New Architecture in the Nineteenth Century,” Architectural History 50 (2007), 1-29. 5 Spyros Papapetros, “On the Biology of the Inorganic: Crystallography and Discourses on Latent Life in the Art and Architectural Historiography of the Early Twentieth Century,” Biocentrism and Modernism, edited by Oliver Arpad Istvan Botar, Isabel Wünsche (London: Routledge, 2011) 77-106. Spyros Papapetros. “On the Afterlife of Crystals,” On the Animation of the Inorganic: Art, Architecture, and the Extension of Life (Chicago: University of Chicago Press, 2012) 113-160. Amy Kulper, “Architecture’s Lapidarium: The Life of Ten Geological Specimens in Architecture,” The Anthropocene, edited by Etienne Turpin (Michigan: Open Humanities Press, 2013), 87-110. 6 Rosemarie Haag-Bletter, “The Interpretation of the Glass DreamExpressionist Architecture and the History of the Crystal Metaphor,” Journal of the Society of Architectural Historians vol. 40, no. 1 (1981) 20-43. Gyorgy Kepes, “Thing, Structure, Pattern, Process” and “Transformation, Physical, Perceptual, Symbolic,” in The New Landscape in Art and Science (Chicago: Paul Thebold, 1956). 7 Georges Teyssot, “Toward a Cyborg Architecture,” A Topology of Everyday Constellations (Cambridge: MIT Press, 2013) 183-218. Alfred Neumann, “Architecture as Ornament,” Zodiac 19 (January 1969) 90-98. Ann Tyng, “Geometric Extensions of Consciousness,” Zodiac 19 (January 1969), 130-162. 8 Frank Lloyd Wright, An Autobiography (New York: Duell, Sloan and Pearce, 1943) 13-14. Frank Lloyd Wright, A Testament (New York: Horizon, 1957) 19-21, 63, 100, 206-207, 220, 300. Edgar Jr. Kaufmann, “Form Became Feeling: A New View of Froebel and Wright,” Journal of the Society of Architectural Historians 40 (1981), 130-137. Richard C. MacCormac, “The Anatomy of Wright’s Aesthetic,” Architectural Review 113 (February 1968) 143-146. Richard C. MacCormac, “Froebel’s Kindergarten Gifts and the Early Work of Frank Lloyd Wright,” Environment and Planning B, no. 1 (1974) 29-50. Stuart Wilson, “The ‘Gifts’ of Friedrich Froebel,” Journal of the Society of Architectural Historians no. 26 (December 1967) 238-241. Edgar Jr. Kaufmann, “Centrality and Symmetry in Wright’s architecture,” Architects’ Yearbook 9 (1960), 120-131. 9 Jeanne Spielman Rubin, “The Froebel-Wright Kindergarten Connection: A New Perspective,” Journal of the Society of Architectural Historians vol. 48 no. 1 (March 1989), 24-37. 10 Frank Lloyd Wright. “In the Nature of Materials,” in Architecture Culture 1943-1968, edited by Joan Ockman (New York: Rizzoli, 1993), 37. 11 Ibid. 29.