Mystery of Symmetry - Exploring symmetry with Snow Crystal


Symmetry is appeared to anywhere in the nature. Trees, flowers, also human being is created symmetrically. Snow crystal is also one of the example of symmetrical existence in the world.  But why the universe create things as symmetrically? Why scientists think symmetry is important? 

Leonardo da Vinci's 'Vitruvian Man' (ca. 1487) is often used as a representation of symmetry in the human body and, by extension, the natural universe. public Domain from Wikipedia

What is the symmetry? According to Colm Kelleher atTED-Ed, difinition of a symmetry is that a transformation that leaves that object unchanged.(1) For example, when the triangle is rotated 120 degrees around an access through its center, people recognize the triangle that is identical to the original. But when the triangle is rotated 90 degree, people don’t recognize the triangle that is identical to the original. This is the symmetry of example in this movie.
And this symmetry has something to do with many aspects of our world and our life. For example, biologists see the type of symmetry and try to understand evolution(1) Depends on the type of symmetry, the body structure is different depends on organisms and these structures Shows the animal’s lifestyle(1)

Symmetry has also something to do with the beauty and it’s also the important sign for human to survive. For example, deformed crops would be dangerous to eat. Our ancestors evaluated if they can eat them or not by checking symmetry(2) Human’s symmetrical face shows the sign as healthy and fertile mating partner(2) Symmetry is very common feature for fauna and flola. (2) The beauty brings us some good feeling because it's essential sign of surviving (2) . Although there are more reasons why beauty makes us happy, symmetry is one of the reason to makes us happy.

Also physisists try to find the truth of universe using the theory of symmetry.  Physicists clearly recognize that symmetry is important to their research of a unified field theory(3) 

Okay, then let's see about the symmetry of snow crystal. Johannes Kepler, who Theorized about the symmetry of snow crystals for the first time thought that Learning what principle makes snow flake symmetry is very variable(4) He thought that symmetry of flower and snow crystal Looks similar but mechanism is different as flower is alive and snow crystal is not alive (4).
Each organisms has unique structure to shape symmetry, but snow crystal is just simple material.So Kepler thought that it’s worth to think about the beginning of symmetry of Snow crystal. (4)
He also recognized that both snow crystal and mineral crystals has similar structure such as faceted structure.(4)But he said science had not caught up yet to explain this structure at that time.(4)

Faceted structure is everywhere in our life. There’re a lot of kind of faceted structure surrounded in the nature.There’s Not only ice, but also copper, diamond, a lot of kind of  crystals.Although different angle shapes different faceted structures, these structures has symmetry inevitably,(4)

So compared to symmetry of organisms structure, The symmetry of snowflakes is directly followed by the mathematical principals in nature. It originates from structure of ice crystals, which is due to the geometry of how water molecules are bound. (4)This is dictated by quantum mechanics which explains how atoms exert chemical bonding forces.(4)
As Kepler says, questioning the symmetry of snowflakes is worth because it’s connected to questioning the truth of nature.