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TRANSFORMATION SYMMETRY
 A triangle can be rotated 3 times

Transformation refers to the actual creation of the pattern through movement.  We will investigate rotational symmetry, mirror (reflection) symmetry, and translation symmetry.  Movement helps to see the symmetrical relations.  In science they refer to the movement by different notation, n- fold (n = repeated faces).  This is used to describe large and small crystalline structures.

 Translation of pattern shown by vector (arrow) showing direction and distance

Rotational symmetry occurs when an object rotates around a point and the object still looks the same. The number of times a face is repeated will depend on its symmetry.  A triangle has a 3-fold rotational symmetry.

Mirror or reflection symmetry refers to a face that is identical but reversed in orientation.  The axis reflects a face from one side of the object to the other is called a mirror plane.

Translation symmetry refers to a slide movement of a figure in a specific direction for a specific distance.  Translations can be described by a translation vector to describe distance (its length) and direction it is pointing.

Symmetry is important in understanding the properties of different matter, especially at the elemental or compound level

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