Lesson 3 - Page 2




Pentagonal symmetry


Plane symmetry moves all points in a plane and preserve distance, angles, shape and size.   Line of symmetry divides a figure into two congruent or same parts.  If the line is extended to a plane, then one side is equal to the other side.   A square (2 dimensional) has 4 planes of symmetry but a cube you can find 5 planes of symmetry.  Plane symmetry refers to a “cut” through an object that is compared side by side.  For example a mirror plane creates an image that is equal but opposite and identical from one side to another.  You may think there are many planes of symmetry, but it all boils down to a 2-fold, 3-fold, 4-fold, or 6-fold axis. 

There are many ways to classify symmetry, below are just a few common types.

 Bilateral symmetry is when one side looks like the other or is a mirror imagine.  Humans are bilaterally symmetrical.  If you make an imaginary line from the head to the ground; one side basically looks like the other.  However if you look at the organs inside a human, they are not bilaterally arranged.  

Radial symmetry is when all segments are equal that radiate from a point.  A ball or a circle has radial symmetry.  Note that all objects that have radial symmetry also have bilateral symmetry.  Radial symmetry also has an infinite number of planes.

Pentagonal symmetry reflects a five-part division.  The echinoderms (sea stars, sand dollars) are an excellent example of pentagonal symmetry in nature.  This is easily recognized as a “star” shape.  Internally, echinoderms also have five part symmetry.

Hexagonal symmetry is a six-part division.  If we rotate the object 1/6th of a whole turn we would view the same identical view.  A snowflake (or ice crystal) has a hexagonal symmetry, although the pattern is different.  Wilson “Snowflake” Bentley (1865-1931) spent 40 years documenting over 5000 snowflakes.  He found all had hexagonal symmetry but not one has the same pattern.  

Cubic symmetry  is  highly symmetrical and found in crystals, art forms, and everyday objects.  This applies to a three-dimensional object. 

Snowflakes photographed by Wilson Bentley



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