Re: Snowflakes
With the courtesy of Wikipedia, here is the definition of a regular hexagon, just for those super brains who do not know what an equilateral polygon is :-
A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).
The common length of the sides equals the radius of the circumscribed circle, which equals (2xsqrt3)/3 times the apothem (radius of the inscribed circle). All internal angles are 120 degrees.
A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflection symmetries (six lines of symmetry), making up the dihedral group D6.
The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side.
From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.
NOW, why does Nature love this mathematical shape ?
Instead of persecuting the OP for raising a very scientific question, strain your limited brain capacity and answer that, if you possibly can divert from posting insults. There is always hope.
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