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First let me tell you a bit more about geodesic domes and spheres.

The word geodesic refers to the shortest distance between two points on a curved surface, and it comes from a Greek geo-, earth, + daiesthai, to divide; thus we have "earth dividing" domes.

Simplest geodesic dome and sphere is based on icosahedron. Icosahedrons have 20 equilateral triangle faces that form very roughly a sphere.

They are called Frequency 1 or 1V domes. Frequency of a geodesic dome indicates how many times each side of the base triangle is subdivided. For example: frequency 3 means the base triangle is divided into 3 lengths, thus forming 9 triangles. It is easy to understand when you look at the drawing:

The Higher the frequency (or number of divisions), the closer the shape is to the sphere. It looks less “pixelated”.

 As a compromise between the complexity of construction and visual impact of the form, I choose to make 3V sphere.

3V sphere is formed from 20 hexagons and 12 pentagons (think soccer ball), divided into triangles. (6 triangles for each hexagon, and 5 for pentagons). Here is where things start getting complicated....the length of the edge of the triangle ( a "strut" in dome language)  varies pending on whether it forms a hexagon or pentagon, or connects them.

3V sphere has 3 lengths struts. I called them A, B & C and colour coded them A green, B blue and C red.

Still with me?? There are lots of web based calculators available that will calculate the lengths of struts, radius of the dome or angles, which is GREAT, as I glaze over those mathematical formulas.

The challenge is that I want to make each triangle in clay - which will need certain thickness - so I need to figure out not only the length of the triangle edges, but the angles as well, so that my clay triangles form a sphere rather than a flat surface.

Now that I know the sizes and angles, next step will be to design triangular components I can make in clay and decide on the making techniques. Fun! Fun! Fun!