Don Caspar – we've mentioned before that he had the first X-ray picture of Tomato Bushy Stunt Virus which showed icosahedral symmetry. And so we discussed why icosahedral symmetry, and one of the reasons is sort of obvious, which we suggested in our first paper on polio, the one that you and I wrote in '59. That if you want to... economical use of genes, then you make many copies of products of a gene. And icosahedral symmetry symmetry uses 60 identical sub-units... which is more than you can use for the others, so it's much more economical to build a shell out of icosahedral symmetry. But then, later, during that time when we... after we published the polio picture... the polio paper, I had a letter from... an acolyte or a pupil of Buckminster Fuller, the inventor of geodesic domes. And he read the polio paper and he sent me a book called The Dymaxion World of Buckminster Fuller. And I knew a bit, I'd seen geodesic domes and I looked through it. And I came... I saw that he had... his language was most arcane; you had to translate it into English. He'd talk about omni-dimension, multi something or other. But then you actually look at the structures he made in the geodisic domes, he maintained that they had identical units and he was building great big domes, one of them had 270 units in it. Now, with perfect geometry you can only build 60 units absolutely identical... identically situated in a dome. And I could see from his pictures that they were... this one had 270; and he said, 'They were all identical.' But if I looked very carefully... I looked carefully at the diagrams and the 270 actually were 240 plus 30. The 30 were on two-fold axes of symmetry so really two half rods and the 240 were four groups of 60. And they were connected by a system of strings; they were what you call tensegrity domes. And the strings had little turn buckles that you use in sailing, fixing ropes; I didn't know, I thought they were little wheels so I misread the picture. And I came to the conclusion how clever the strings, which are tied to the ends of the rods and the rods are moved by strings, because I knew you couldn't have more than 60 identical. I thought, 'These... these were little rollers which adjusted the length of the strings to build', and I realised that this was a way of building something with more than 60 units. By which time... we knew by this time the Turnip Yellow Mosaic Virus which we'd been working, had at least 150 sub-units and so it had to be. So I began to think, I know there were controversies, Roy Markham said there were 32 times five, there were five, which wasn't correct for that; and I realised that I invented the term quasi-equivalence. And now Don Caspar, in the States, had also been wondering about this problem and he'd built models in which he was building... allowing... he had cardboard models which were really like ice cream cones with flat faces and he was showing you could put them in... into ways with more than 60 units. So we both had the idea independently but we arrived at it in different ways. So we wrote a paper in 1962 and it was written and we gave it at the Cold Spring Harbour Meeting in '62, it was called Physical principles and the design of virus shells and protein shells of viruses [sic].
