From HENRY DURAND
It may seem odd that ‘chemists’ do not realise that no polyhedron can
be made out of regular hexagons; this isn’t really a matter of Euler’s formula,
but stems from the simple con-sideration that 3 x 120 degrees = 360 degrees.
You get then a beautiful flat pavement. Of course, Euler goes further and
explains that no convex polyhedron can be built even with irregular hexagons.
It is a pity that 3-D geometry has been largely dropped from high-school
teaching (at least, it is the case in France). If Smalley, Kroto and the
rest had heard of Euler’s formula (as I did some 40 years ago), they would
have been saved a night-long exercise with scissors, toothpicks and glue
(but would have missed a beer drinking party).
Henry Durand University of Paris France
