Six is indicated by the Latin prefix sex-, as in sextic, or by the Greek prefix hexa- (-), as in hexagon,
hexagram, or hexahedron.
The six-fold symmetry is typical of crystals such as snowflakes. A mathematical and physical treatment can be found in Kepler (Halleux 1975), Descartes (1637), Weyl (1952), and Chandrasekharan (1986).
Chandrasekharan, K. Hermann Weyl (1885-1985): Centenary Lectures. Berlin, Germany: Springer-Verlag, 1986.Descartes,
R. Discours de la méthode: Les météores. Leyden, Netherlands,
1637.Kepler, J. Étrenne ou la Neige sexangulaire (Trans.
R. Halleux). Paris, France: J. Vrin Éditions du CNRS, 1975.Wells,
D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, pp. 67-69, 1986.Weyl, H. Symmetry.
Princeton, NJ: Princeton University Press, 1952.
), and the third triangular
number (
). It is the also smallest perfect number, since 
. The number 6 arises in combinatorics
as the binomial coefficient 
, which appears in Pascal's
triangle and counts the 2-subsets of a set with 4 elements. It is also equal
to 
(3 factorial),
the number of permutations of three objects, and the order of the symmetric
group 
(which is the smallest non-Abelian
group).
-), as in hexagon,
hexagram, or hexahedron.
