With a large 3 frequency dome its important to build a model to follow as things can get complicated. I had made one of these before using straws and sticky-back plastic so got myself loaded up with straws from a supermarket. All the straws I could find had stretchy bits near the top so I cut one to find a maximum strut length I could use. To cut a long story short I came up with a dome radius 35.25 cm for my model.
If you have seen the basic guide to making a model icosahedron you will see it is made up of 20 faces. In a two-frequency dome, each strut length is subdivided by two, creating 4 equilateral triangles on each face.
For the 3 frequency icosahedron each strut length is divided by 3, creating 9 triangles, made up of struts as shown in the diagram below.
In a 3 frequency icosahedron there are 3 chord factors ie three different strut lengths are required. If you get different coloured straws the model works as a useful reference for building full scale. The chord factors for a 3 frequency icosahedron are:
- A = .3486
- B = .4035
- C = .4124
And that formula again: C (chord factor) x R (radius) = length of strut
My sums for the struts were:
- A= 123mm x 60, colour blue
- B= 142mm x 90, colour green
- C= 146mm x 120, colour orange
It took me an hour and a half to cut these and pretty soon I had three piles of straws in front of me, waiting to be connected. I started by connecting the C nodes. I then started connecting the B and C struts, to make a single icosahedron face. Then I went into factory mode and made all of the C connections.
Bit by bit, the dome took shape and I used a camera tripod to hold the model in a rough dome shape to make all of the connections. Eventually, I had my model three frequency icosahedron.