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
Probably Johann Kepler was the first to remark this hexagonal symmetry in snow
flakes, and he wrote a book about it for his money-lender (in 1611).
In the world of the animals the regular hexagon can be seen in the honey-comb and as
the radiate 3).
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.