Escher-type Tessellations by Reflection
Using a Rectangle

Polygons that can be used:

Any rectangle

Types of symmetry found:

Translational symmetry
Rotational symmetry
Reflection symmetry
Glide-Reflection symmetry

Technique:

1. Start with the left side. Draw any type of line design from one vertex to the midpoint along that side. Rotate that design around the midpoint (180 degrees), and trace the design to finish the side.

2. Choose one of the two sides that are left, and draw a line design from one vertex to the other. Translate, or slide and trace, this design to the opposite side.

3. The fourth side will serve as the line of reflection. Flip the design over this line and trace. You should end up with a tessellation piece with a vertical line of reflection in the center.

4. You now have a completed tessellation piece. Use your imagination to decide what your piece looks like and fill in some details.

5. On a piece of paper trace out the shape near the center of the paper. From there, continue to fill the entire piece of paper with the tessellating shape, as though you where building a puzzle in which all of the pieces were the same.

6. When the paper is completely covered with the tessellation, add in the details from step 4. You may wish to use different colors or designs to spice up the picture.

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