Snowflakes are six-sided, and Johannes Kepler wrote the first serious attempt at explaining why: a short book of 1611, Strena seu de nive sexangula, offered as a new year's gift, in which he asked what makes every flake six-cornered and proposed that it arose from the packing of small identical units. He had no way to confirm it. He was right in outline, since the hexagonal symmetry does come from the arrangement of water molecules in ice, and the same short book contains the sphere-packing conjecture that carried his name until Hales proved that as well.
Hexagonal structures recur because they are what equal units under pressure tend to produce. Basalt columns at the Giant's Causeway and at Fingal's Cave crack into rough hexagons as lava cools and contracts. Insect compound eyes, some bird bone, graphene and the cells of a beehive share the pattern for related reasons of packing and economy.
In Judaism the six-pointed star, the Magen David, is two overlapping equilateral triangles with a hexagon at the centre. Its adoption as the principal Jewish symbol is late. The shape appears in many contexts, Islamic and Christian among them, for centuries without any specific Jewish meaning, its use as a communal emblem is documented in Prague from the fourteenth century, and it spread widely only in the nineteenth. Anyone dating it to Solomon or David is repeating a legend.
In Islamic geometric ornament the hexagonal grid is one of the principal underlying frameworks, generated in practice by exactly the compass method described above and elaborated into star patterns of six, twelve and twenty-four points.
Chinese divination uses the sixty-four hexagrams of the Yijing, figures of six lines each, though these are stacked lines rather than hexagonal geometry, and the connection to the polygon is verbal rather than formal.
Sources Strena Seu de Nive Sexangula (On the Six-Cornered Snowflake)Johannes Kepler with The Star of David: History of a Symbol, in The Messianic Idea in JudaismGershom Scholem, The Topkapi Scroll: Geometry and Ornament in Islamic ArchitectureGulru Necipoglu, Fathoming the Cosmos and Ordering the World: The Yijing (I Ching, or Classic of Changes) and Its Evolution in ChinaRichard J. Smith