This and the other image nearby are from Kepler's pamphlet
on snowflakes. Contrary to what one might think at first.
they are not of two dimensional objects, but rather an attempt
to render on the page three dimensional packings of spheres.

In his book De nive sexangula
(`On the sixsided snowflake') of 1611, Kepler asserted that the
packing in three dimensions made familiar to
us by fruit stands
(called the facecentred cubic packing by crystallographers)
was the tightest possible: Coaptatio fiet arctissima:
ut nullo praetera ordine plures globuli in idem vas compingi queant.
He didn't elaborate much, and his statement lacks precision.
It is almost certain that he had no idea that this assertion
required rigorous proof. At any rate, this claim came to be known as
Kepler's conjecture, and it turned out to be extremely
difficult to verify.

Kepler quite likely would have thought that the analogous assertion
about the hexagonal packing in 2D was
even more obvious. However, it
took about 300 years before it was proven,
by the Norwegian mathematician Axel Thue.
It is arguable that it took that long just to understand
that such an `obvious' assertion required proof.
It took another century before a proof of the much more difficult
claim about 3D was found, by Tom Hales.

Both images are from photographs taken of
the copy of the original edition of Kepler's
pamphlet now located at the Thomas L. Fisher Library at the University
of Toronto.

