Blunder

Or more haste less speed. Or festina lente, as they used to tell us at school.

The argument used at reference 1 depends on the existence of something there called the triangular projection, a projection which, in effect, triangulates the surface of a sphere into a large number of identical equilateral triangles.

It came to me this morning that such a projection may not exist, and subsequent investigation revealed that huge amounts of work have been done on this and related problems. Reference 2 is a good taster, from the University of New South Wales - of which I read that 'University of NSW head Ian Jacobs received a salary just shy of that, with $1.22m'. It looks as if we are not the only country with trouble on that front.

The good news is that there are plenty of quite good approximations to my triangular projection, so I assert without proof that the argument at reference 1 could be successfully adjusted.

Reference 1: http://psmv3.blogspot.co.uk/2017/09/sensing-spheroids.html.

Reference 2: http://www.maths.unsw.edu.au/about/distributing-points-sphere.