So I came up with the idea to make my third buckyball, a truncated icosahedron requiring 90 struts, this time using 6 colours. With the two colours versions I already found out how to structure different colours, and I had at least a plan. There's 12 pentagons in the buckyball shape (which is basically the same layout as a soccer ball), and 20 hexagons. Using six colours means each hexagon can contain all colours.
I thought if I start out with the pentagons, each build in a single colour, it should work out in this way. It still turned out as some tricky puzzle, and the actual build took me as long as the preparation of all the elements.
After building the twelve pentagons, 60 struts were gone, and 5 five struts of each color left. Each hexagon in this tensegrity consists of the struts from a adjacent pentagon, and three that connect to another hexagon. I had to figure out a build algorithm that allowed the hexagons contain all colours, which took me only two attempts.
There are two pentagons of each colour, and as expected, they appear on opposite poles of the finished structure. To my surprise, the remaining five struts of the same colour form an equator, only this configuration warrants that each hexagon contains all colours. This symmetric distribution of colour doesn't continue with the hexagons, all of them seem to have a different variation in the way the colours are arranged.
While I expected to have at least two hexagons in 'rainbow configuration' (yellow, orange, red, purple, blue, green), it might not be possible to achieve this, but I really can't be bothered to reassemble this sphere, or to transform this into a mapping problem. The weight means it's best to suspend this sphere, which measures roughly 45 cm from pole to pole with 20cm struts.
|Rainbow buckyball (90 struts)|