
The regular hexagon can be divided in three regular triangles, so that the figure is easy to construct with a pair of compasses. Already the Greek group of Pythagoras knew that a plane can be filled with regular hexagons.
At the age of 16 Pascal proved
a theorem (later called after Pascal), for a hexagon inscribed in a
conic section: the cuttings of the opposite sides lie on a straight line: the
line of Pascal. In chemistry the regular hexagon is the formula for the benzene ring. It is made of six carbon atoms, bound in a ring by a hydrogen atom between each neighbor. Also some crystal structure have a regular hexagonal form, for instance zinc sulfide and a special form of diamond. In real life we see the regular hexagon in the ice crystals by which snow is
formed ^{2}.
Probably Johann Kepler was the first to remark this hexagonal symmetry in snow
flakes, and he wrote a book about it for his moneylender (in 1611). In the world of the animals the regular hexagon can be seen in the honeycomb and as
the radiate ^{3)}. notes 1) Known as the 'hexagramma mysticum'. 2) All snow flakes have sixfold symmetry, some kinds of snow flakes have the form of a hexagon. 3) An unicellular animal with a silicon skeleton. 