an icosahedron primer

What is an icosahedron?

An icosahedron is a 20 faced spherical shape recognised even by Ancient Greek mathematics – it is one of the Platonic Solids, which are: Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron (see more about this).

An icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is a form found in nature, for example some viruses have icosahedral shells.

Ever since I learned about Buckminster Fuller at art college, who developed structures called ‘geodesics’ based on the icosahedron and other three dimensional structures, I have wanted to experiment more with making human-scale geodesics. So a first stage to ‘understand’ this shape is to build a basic model, this time using cardboard.

Firstly, draw out 20 equilateral triangles in the shape shown in the first picture:

Draw flaps around the edges of each triangle so that you can stick them together with a glue stick. Then cut out the shape and make some creases along the lines so that the icosahedron can find its shape:

Then start gluing the tab surfaces to the triangles to form a spere shape fom the cardboard. You may need to trim off some of the tabs as you go – you should end up with something like this:

I have drawn additional lines onto the shape to show how you can have different frequencies of geodesic dome, by subdividing the large equiliateral triangles. The smaller the triangles which go to make up the dome, the more it tends towards a sphere.

So this shape is the basic plan for my first greenhouse. As you can see from the above picture, you can ‘slice’ the isocahedron to make sub-shapes. In this case I will take the top five eights of the shape and create a frame using wild hazel from hedgerows, covered in polytunnel material.