Buildings in which we conduct our lives are mostly structures created from rectiliniar elements joined at right angles. Many find this boring – the implication being that buildings have an obligation to entertain and amuse.

This leads to yet another restatement of the building-architecture divide. “Buildings are boring. Architecture isn’t.” Architecture is thus granted licence to delight us, stimilate us, entertain us, divert us and generally amuse and, like it or not, this is how architecture is conducted in today’s media theatre which, come to think of it, is the only theatre that seems to matter. When the media theatre is the only theatre in which the performance of architecture is validated then, other than for the degree they impact upon the media, the activities of private practice and academia are meaningless. It’s the butterfly in the rainforest syndrome. Does architecture exist if there isn’t a link to click on? How did we get here?

A non-rectilinear geometry isn’t sufficient to make a building architecture. Lighthouses and castles each have special geometries that create structures and construction that may not be architecture but are very suited to hostile environments, for example. Television towers have special geometries that provide other required characteristics such as height and stability.

Buildings with non-rectilinear geometries are only architecture if they use a non-reclinear geometry for the sake of using a non-rectilinear geometry, i.e. because they can. This is where technology enters the frame. New technologies continually extend the range of what can be done, without questioning whether it should be done. The application and/or misuse of new technologies has been taken as a sign of a building being “of its time” if not ahead of it, even though this can only be decided only in retrospect. In general, we’re too quick to think things are ahead of their time.

Hexagons occur naturally and were one of the first alternative geometries to be appropriated by architecture. Nature is full of sixes. Nature is sixes and there’s nothing more organic than carbon, even though benzene may not be one of our favourite compounds. The trouble with chemical bonding is that it occurs at the molecular level – it’s too small to see. Organic compounds are us, but we have no experience of them. The actual chemistry of organic Nature has nothing to do with what we see or want to see as the representation of organic compounds, things representing the processes by which organic compounds are made, or things representing an architect’s “familiarity” with the processes by which things made of organic compounds organise themselves.

Then there’s the hexagonal crystal family that includes quartz, dolomite and beryl but the problem with crystals is that they’re solid. They take up space. They don’t enclose it.

Snowflakes have a hexagonal geometry and no two are exactly alike. This ought to make them prime candidates for architectural appropriation but snowflakes unfortunately occupy only two-dimensional space. Believe me when I say the internet is a huge repository of snowflake imagery.

Honeycomb is the perfect analogy for a “natural” architecture. Honeycomb encloses space for a purpose and is made by industrious bees that like flowers. Honeycomb is more than just a plan. These next images show how the bases of the cells convert the six sides into rhombi that interlock even more ingeniously back-to-back.

Somewhere between outgrowing his Froebel blocks and becoming obsessed with circular geometries, Frank Lloyd Wright became obsessed with hexagonal geometries. Hexagons were either his way of rebelling against the tyranny of rectilinear geometry or of wanting to be seen as rebelling against the tyranny of rectilinear geometry. Nature was invoked and, for Wright, this meant that hexagons were in some sense “organic”.

This is Giant’s Causeway in Northern Ireland. It’s igneous rock that rapidly cooled into hexagonal columns. It’s 100% natural but, basalt being basalt, is 100% INORGANIC.

The Giant’s Causeway is an area of about 40,000 interlocking basalt columns, the result of an ancient volcanic eruption. It is located in County Antrim on the northeast coast of Northern Ireland

But whether organic or merely natural, the use of hexagonal geometry rather than an orthogonal one soon came to denote creativity – the untrollable urge to not go with the flow, to be wild, unconventional – in much the same way as Wright himself. Many houses of different sizes were to come but Bazett House was first.

The full hexagon didn’t last long and Wright was soon to instruct his unpaid staff to graph-up in rhomboids. It mostly worked, apart from staircases, cabinetry, beds … We can only guess at what advantages such design may have had. It’s unlikely to have been construction. Swimming pools and floor tiles can be forced into a hexagonal grid but elements such as cabinetry and staircases composed of linear elements don’t fit naturally into 120° angles.

Wright’s 1941 Richardson House was up for sale recently so we can have a look around (courtesy of Curbed). See what I mean about beds and cabinetry?

The larger rooms are the more successful and, even ignoring the nice piece of property outside, seem like pleasant spaces to be in.

Wright’s 1956 Price Tower attempts to contain a 60° geometry within a 90° geometry. Apart from the tricky staircase and the absurd elevators it’s mostly successful due to the mediating effect of sin 30°. You can see Wright falling out of love with hexagons and in with rhomboids. Even so, the rhomboid grid is becoming fainter.

Possibly due to him being dead, Wright abandoned both hexagons and rhombi by the end of the 1950s but his influence on John Lautner lived on in Lautner’s 1960 Malin House. Unlike Wright’s hexagons, Lautner’s octagon can at least be rationalized in terms of structure and construction.

At the far end of the 1960s is Jean Renaudie’s 1969 Jean-Baptiste Clément Housing that’s more about triangular geometry than it is equilateral triangles or combining them into hexagons.

Inbetween is Lautner’s 1963 Goldstein House and its selective use of 30°, 60° and 90° geometries according to wow requirement. You’ve seen the photos.

Lautner and Renaudie mark the tail end of prismatic geometries as indicators of architectural innovation. Angular geometries went out of fashion and circular geometries came in but they weren’t Wright’s ornamental or curly circles but circles with a structural rationale. Pier Luigi Nervi’s Rome Basketball Stadium for the 1960 Olympics is the one mentioned most, but there were also soon-forgotten buildings like Sir Roy Grounds’ 1959 Academy of Science Building in Canberra. Eero Saarinen’s 1955 Kresge Auditorium is better remembered.

There was only so much that could be done with a circular shell. Words such as hyperbolic parabaloid re-entered the architectural lexicon. This is Felix Candela’s 1958 Los Manantiales Restaurant near Mexico City.

Tensile structures offered more new geometries. Wright at least claimed his Usonian houses had a wider applicability whether they used an unorthodox geometry or not but these new geometries did not pretend to be anything but unique. Many exceptional structures were produced using tensile structures but they remained exceptions. The 1957 Sunpu Kaikan in Shizuoka City and the 1963 Basketball Stadium for the Tokyo Olympics were both by the exceptional team of Kenzo Tange and Yoshikatsu Tsuboi. [c.f. “Unsuung Hero: Yoshikatsu Tsuboi“]

Saarinen was there too with his 1958 Ingalls Ice Hockey Stadium.

In 1955 Saarinen was commissined to design the TWA Flight Centre at New York’s JFK so it was no surprise he championed the freeform geometry of Jørn Utzon’s Sydney Opera House as winner of the 1957 competition. The famous non-geometry famously underwent a series of rationalizations to define the curved shells as segments of a spherical surface. Some say it lost something in the transliteration. Six of one.



SZ107, Red book, Opera house



By 1973 and the time it eventually opened to requisite fanfare, Sydney Opera House was a creature from another era. Frei Otto’s Olympic Stadium had been completed the year before, ushering in a new breed of structure. Stadia were perfect for testing new geometries – perhaps because their functional requirements amounted to little more than keeping rain and/or sun off a majority of the spectators. The same 1973 featured architectures as diverse as Ant Farm’s House of the Future in Texas, Arata Isozaki and his post-Metabolism in Japan, Aldo Rossi and his Neo-Rationalism in Europe, and either an SOM Corporate or a Post Modern something just about anywhere. Even John Lautner had gone freecurve with his Arango House in Acapulco.

Building shells and structures could now be made to assume any shape a designer wanted them to and nobody wasted time imitating honeycomb anymore. To have a geometry of any kind was now conventional somehow. The hexagon, that most obvious and least troublesome of the non-perpendicular geometries was no longer the sign of a maverick creativity. The bar for “natural” and “organic” shapes was re-set to a level beyond the needs of any living creature and for chemistry to have the chemistry for.

Fact: Carbon being carbon, the building blocks of life are regular, repetitive, and symmetrical. There’s nothing “organic” about organic structures and there’s nothing organic about “organic” architecture and nothing natural about “natural” architecture. It’s as superficial natural as tendrils of Art Nouveau ironwork.

Despite its claims to be the future of architecture, I see Parametricism as a kind of Art-Nouveau throwback marking the end of an era where ‘cutting edge’ or, if you will, “avant-garde” architecture could only be indicated by a succession of contrived geometries, each one re-representing the future of architecture.

By being able to generate anything one wants to, Paramtricism is the conclusion of that particular sequence and, as such the end of geometry. “You want curvy? At your service!” “Perhaps some funky angles? No problem!” There are now infinite possibilities to narrow the definition of architecture.

As the possibilities for geometric invention increased, their scope for wider application across the entire field of architecture became progressively narrower. This is why the 1950s glut of stadia. Stadia aren’t everyday buildings but lend themselves to geometry or any other ornament one cares to apply as long as the relationship between the observed and the observers is satisfied. Despite FIFA’s best efforts, there’s not much demand for stadia so the object of geometric virtuosity is more likely to be an opera house or an art gallery. When architectural invention is seen only in terms of geometric invention, there are fewer and fewer buildings to which that invention can be applied, and with only intermittent benefit to fewer people. [Here, I’m assuming the purpose of architecture is to be of use to others but I may be wrong on that.]

This dysfunctional situation where architecture is only possibile for fewer and fewer types of buildings is dependent upon the producers of architectural imagery convincing the consumers of architectural imagery that architectural invention and geometric invention are one and the same. By everyday reminding architects to see architecture in this way, the very tools that architects work are complicit.

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The header image is of Kaiser Wilhelm Memorial Church in Hamburg, Germany. The original neo-romanesque chuch was completed in 1895, almost completely destroyed in 1945, and remained a ruin until 1956. The octagonal church and hexagonal bell tower were completed in 1956 at the time when prismatic geometries were about to be replaced by shell structures and then by tensile structures. The structure does not look sixty years old, perhaps because it was detailed and built with materials resistant to ageing and to a crystalline geometry having no particular time stamp.

misfits' architecture, published on April 2, 2018, accessed on September 23, 2020, permalink: Cite this article as: Graham McKay, "The Hexagon [a eulogy],", published on April 2, 2018, accessed on September 23, 2020, permalink: https://misfitsarchitecture.com/2018/04/02/the-hexagon/