The invention of the geodesic dome is credited to Buckminster Fuller but is reported to have been invented 25 years earlier by Walter Bauerfeld for work on a planetarium projector at Carl Zeiss optics. I ‘discovered’ them at art college through R. Buckminster Fuller and his amazing inventions.
Geodesic domes, to me, are quite beautiful. Lightweight and strong, they make very efficient use of materials which suits my pragmatist take on things. Geodesic domes are elegant and sophisticated structures. Deceptively simple to look at they hold a whole realm where art, craft, science, mathematics and nature peacefully co-exist. Fuller originated his mathematical principles of domes from observation of nature.
I had made some geodesic dome structures before, but never for a greenhouse: a 2 foot dome at art college made from drinking straws, a two metre dome out of garden sticks to grow over with sweet peas, some smaller models.
Every day my springer spaniel, Freya, needs a walk so often when we went I out I would take a saw and find and cut myself the longest length hazel rods of a useable diameter I could find, (in addition to providing numerous sticks for the dog).
Over the course of a couple of months of winter I built my collection of long, straight hazel sticks up to the 30 I needed for the icosahedron. I trimmed them down to an optimal length which came out at 196cm. Normally you would work out the size of the dome you wanted and calculate the strut length from this – but things don’t work quite the same with wild materials.
The reason for this seemingly arbitrary measurement is just so that I could choose the optimum length of stick available in the hedgerows. I just built the icosahedron with these and came out with a fair size greenhouse dome with a diameter of 315cm, an internal height on the inside edges of 165cm sloping up to 230cm in the middle. To add strength and stability (and to compensate for using ‘natural’ materials of irregular shape) I added a central pole to the structure.
For the more scientifically orientated of you, this intuitive dome making is hardly instructive. The icosahedron has 30 edges of the same length, in dome making these are often called ‘struts’. There is a relationship between the strut length and the radius of the icosahedron. The radius of the dome is slightly less than the strut length. With bigger domes, calculation involves a ‘constant’ called a chord factor and these can vary depending on what sort of dome you want to build. Some constructions, such as the 3 frequency icosahedron I built later, involve several chord factors in a single dome. The chord factor involved in an icosahedron is 0.95 . That is to say the strut length is 95% of the radius.
Firstly though, estimate the diameter of the dome you want to build, let’s say 300cm across, giving a radius of 150. To find the length of strut you need the formula is:
Chord factor x radius = length of strut
0.95 x 150 = 142.65
So you will need 30 lengths of 142.66cm to build a 3 metre dome.
It could be that to avoid the irregularities of ‘wild wood’ you might decide to purchase enough 2 x 1 planed timber to do the job and this is often available in ‘packets’ of 10 ready cut to 200cm lengths. In this case you will need 3 packets (get 4 in case of splits). Your ready-made lengths will give you a dome of these proportions:
Chord factor x radius = length of strut
951 x radius = 200 (200 divided by .951) = 210.3 x 2 = 420.6 diameter icosahedron.
If you estimate sawn 2×1 timber at 2011 prices, that is 65 pence a meter 40 x 65 = 2600 = £26 (which is about $40). So it would be easily feasible to construct this icosahedron greenhouse using planed or rough ‘2×1’ – but I didn’t want to spend any money.
The size of the dome is also going to vary a bit depending on how the struts connect to each other. There are several tried and tested methods for this in dome connection theory (deserves its own article – later). In an icosahedron each vertex (the singular of vertices) joins five struts – a very complicated joint for joining wood to wood, although it can be done. I decided to keep it simple for this one and drilled holes through the end of each piece of wood.