It is not at all tedious if you consider the modularity of geodesic design.Tetra 3, cube4, Icos5,Octa8. You only require one of the triangles to compute all the relationships. Each tri is divided by frequency, ie 4Freq Icos as four subdivisons of each edge of tri and there are 5 of these triangular sections.
So find one of the main triangular sections and discover the modularity of the internal triangles from the corner vertexes. Everything is reflected ! At first it appears complex but the elegance is in the simplicity of it all.
Create an iso tri and begin dividing it up from edge to edge or from vertex to edge.
The formula for chord length is 2r*sinA/2
If you need any assistance