Forma, Vol. 11 (No. 3), p. 161, 1996


The present search for surface-minimising structures has given new significance to the Frank-Kasper structures. These have turned out to be the best candidates, when converted by the dual transformation point (atom) cell. I have therefore been asked how these structures first arose in my own work.
Together with John Kasper, who was well acquainted with some complex alloy structures from their experimental determination, I set out to put some system into their classification. We had both visited Toledo earlier in the year that we met, and both had been struck by the same idea, that Moorish tiling patterns played on the same theme, attempting the impossible, the tiling of the plane with regular pentagons. Some walls in Toledo seemed to accomplish this, up to a boundary, beyond which you could not continue: and a dome in the synagogue succeeds, but on a spherically curved surface. Elsewhere, the tiling with equilateral pentagons is found. A floor in the Glasgow Physics Lab. also shows this pattern, or used to.
Then, between us, we perceived that some alloy structures can be seen as alternate stackings of the equilateral pentagon outline and its dual. Adding in some elementary topology from Euler (inspired, so far as we were concerned, by Cyril Smith), we had a publication. Then I invited John Kasper to come to Bristol for a year, and we wrote another.
In comparing this with recent developments, two thoughts emerge: that in thinking about structures, inspiration can be drawn from surprising sources, and that Cyril Stanley Smith's sowed many of the seeds of such eclectic thought, over more than one generation.

Charles Frank