I''m interested in the theory of Geodesic Domes,
but am somewhat puzzled by the mathematics.
In planning a 3V Icosahedral Dome I would split
each of the 20 triangles into 9 smaller triangles.
Of these, the inner 6 would form a regular hexagon,
and the triangle at each apex would combine with
similar neighbouring triangles to form pentagons
at the 12 original vertices.
My problem is this.
Where do I divide the original edges?
I would have expected to trisect the angle at the
centre of the sphere. Or even to make the central
chord shorter than the outer chords (to give the
pentagons a better share of the surface area).
There must be some reason why all specifications
make the central strut longer than the two outer
There must be some constraint I am missing.
Hoping someone can put me wise.
[ Comments 1 ]
For the 3v icosa, there are a few key means of dividing up each of the 20 icosa triangles into 9 sub-triangles. Take a look at the thread called Tips on geodome V3.
Here's a useful intro to geodesic domes and math.... "Geodesic Domes". 1994. By Borin van Loon. Stradbroke, Diss, Norfolk, UK: Tarquin Publications.
Another is "Geodesic Math and How to Use It", by Hugh Kenner, first published in 1976, reprinted in 2003 (without corrections... boy, those editors at Univ. of California Press were lazy). That book is pretty technical and has quite a few errors. Nevertheless, it's very good.
Then there's Domebook 2, which does a good job of presenting geodesic geometry in a practical way for amateur builders. It was first published by Pacific Domes in May 1971. Now out of print, but you can probably find a used copy via Internet booksellers.
Gerry in Quebec