# The round in the square the hexagon as a mediating shape in architecture

Geometry is a bit like the screw. Somehow it holds everything together, whether on a large or very small scale, from supporting structures to clockworks. Pretty much everyone who builds something should have it handy. The same applies to geometry. In design, art or architecture – even in nature – geometry is the foundation of the greatest variety of forms.

Basic shapes include point, line, triangle or the square. After all, in mathematics, the most exciting things happen right at the beginning of the number line. After that everything is just repetition. For this reason alone, it is always worthwhile to look back at the basics. A form that has received far too little attention is the hexagon. This is not only similar to the circle, but above all superior in architecture. In some respects, even the dogmatic right angle stands on shaky ground against it.

### Efficiently angular

Geometric shapes are often impressive either individually or in combination – the hexagon, however, can do both. Especially as a floor plan, its ratio of perimeter to area is of enormous advantage. Compared to a square ground plan of the same circumference, the regular hexagon has a larger area. Or to put it another way: on the same surface area, a material saving of 7% and thus demonstrably lower heat emission is possible. Also worth noting are the characteristic obtuse angles, because protruding peaks as in the triangle are known to break more easily.

### Tangible geometry

A true advocate of the hexagon was the GDR architect Wilhelm Ulrich. He dedicated his whole life to its possibilities and strongly advocated replacing the right angle that is predominant in modern architecture. In addition to the predictable aspects, he also emphasized the tangible properties of the hexagon. Especially in the living area, the spatial effect is more open and larger compared to the rectangle. In addition, the lighting conditions are more favorable, as natural light enters the room from different angles during the course of the day. A little more privacy is provided by the obtuse room angles of 120° – so the neighboring room easily disappears from view.

But the advantages of the hexagon go far beyond the living area. With the Berlin Philharmonic Hall and the neighboring Chamber Music Hall, Hans Scharoun proved not only an expressive spatial concept for concert halls – but above all the excellent acoustics that emanate from the hexagon by optimally reflecting the sound in the room. Better acoustics and the centered spatial effect are properties that could also help to improve communication and the sense of community in schools or meeting rooms – workshops and discussions often take place in a circle anyway.

### Hexagons create access

Extremely practical inside the room – but also on the outside? Already Vitruvius suggested to base the basic cut for city planning and in fortress construction on polygons, so that an all-round observation and thus better protection against attacks could be given. Nowadays, fortresses are no longer needed, but the rondel-like principle still proves helpful. Tegel Airport in Berlin, for example, with its familiar hexagonal main building, not only provides particularly fast access to the gate in question, but also efficiently coordinates aircraft to their parking position. In Stockholm-Grondal, a settlement has been created with hexagonal, almost enclosed courtyards that protect against the strong sea winds and also provide a center of coexistence and promote almost village-like communities. Here, too, the obtuse angles of the apartments to each other simultaneously prevent the unwanted view of the neighbor.

### The hexagon connects

However, hexagons show true strength when used in combination. Nature famously leads the way, whether in honeycombs, compound eyes or crystalline structures. The reasons are well known: The hexagon is similarly efficient as the circle – in the grid but covering the whole area, completely without losses. Above all, it is extremely stable, as acting forces can be distributed over the entire structure. Timelessly, the grid runs through ornaments, windows or parquetry: From Girih tiles from Islamic culture to hexagonal floor tiles, which are mainly laid at gas stations to avoid displacement during constant starting and braking.

Whether it’s pavement or street layout, the hexagonal grid just lends itself to being a universal tool. In the sixties, Wilhelm Ulrich developed an alternative, hexagonal traffic network without right-angled intersections. The concept guaranteed greater safety through better visibility and smoother traffic flow – unfortunately, many of its suggestions went unheard. But today, new technologies combined with hexagonal geometry promise entirely new possibilities in biomorphic construction. Humans seem to be realizing what nature has always understood as a creative model: Somehow it holds everything together.