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Snowflakes and Kaleidoscopes

Dn (Dihedral) symmetry is when an object has symmetry about different lines. The applet below is an example of this Dn symmetry. You are able to change the angle between the lines of symmetry allowing for different objects to be created. By choosing each point you can change the color. The trace is on allowing for drawing to occur. Examples of objects in real life with Dn symmetry include kaleidoscopes and snowflakes. Did you know that snowflakes line of reflections are 30 degree increments apart. So they could be 30 degrees, 60 degrees, 90 degrees, etc. Can you make a snowflake with this applet? What about a kaleidoscope? How about different polygons? A square? Triangle? Hexagon? What does the angle need to be at for each of these polygons? Are you able to create a Cn symmetry with this Dn applet?Try changing the color and seeing what creations you can make.