A Tessellations is a pattern made from many copies of a shape 
that fit together without gaps or overlaps. 

There are several shapes that will tessellate:  
           a rectangle                                        a triangle                                  and a hexagon.         

Squares    Equilateral Triangles  Regular Hexagons  

Try to tessellate this equilateral triangle by copying it into the Paint program. 


As you can see, the pentagon (green) will not tessellate.  
The heptagon (purple) will not either.

Regular Pentagons Do Not Work            Regular Heptagons Do Not Work

That is...they won't tessellate by themselves.  Check out these beautiful designs created by using a combination of regular polygons.

Semiregular Tessellation: 4.8.8 Semiregular Tessellation: Semiregular Tessellation: 4.6.12
Semiregular Tessellation: Semiregular Tessellation: Semiregular Tessellation:


Let's start in the Paint program using a basic rectangle.
The tessellation you will be creating is called a SLIDE.  You will cut out a piece from one side and slide it over to the other side.  This is also called a TRANSLATION.

Start with a basic square.  Use the line tool to draw the piece you plan to cut out.

Use the  SELECT  tool to select the section you are removing.  Copy and paste it (transparently) on the opposite side.

Erase the appropriate lines.

Fill the shape with color. Select the whole piece and copy and paste the interlocking shapes as many times as you wish.  Use alternating colors to fill the final design.



The next pattern, or tessellation, was created by cutting out a piece and turning (rotating) it around the corner of the shape.  This is called a TURN, or ROTATION.



The tessellation below is called a SLIDE FLIP, or a REFLECTION
It was created by sliding the cut out piece over to the other side, and flipping it over. 
This....  flips to this .