Tessellations by Translation

Polygons that can be used:

Any quadrilateral of hexagon with parallel and congruent opposite sides

Symmetry: 

Translational symmetry

Technique:

1) Draw your beginning polygon. For an example of this tessellation, a parallelogram will be used as shown in Figure 1.

2) Use the pencil to draw a line design from one vertex to another along the top side. See Figure 1.

 
Figure 1 

3) “Lasso” the line design to select it. Copy it and paste a copy. Move the copy so it lines up with the bottom side (Figure 2).


Figure 2

4) Repeat steps 2 and 3 for the left side (moving a copy to the right side), and any other pairs of opposite sides you have, until your piece is done (Figure 3).

 
Figure 3 

5) Erase the lines of your original polygon (in this case, the parallelogram) and any other extra lines so only your design can be seen. You now have a tessellating piece. Add any details with pencil at this time. You may paint the figure now, or wait until you are done tessellating to paint the figure different colors (Figure 4).


Figure 4: Dog barking on a footrest

6) “Lasso” your entire piece to select it. Copy it and paste a copy. Move (translate) the copy so it fits into the original like a puzzle piece. Continue to paste and move your piece until the entire page is covered. (To get pieces to fit off the sides you may need to pick up the piece near its sides.) See completed tessellation.

7) Paint your pieces different colors to distinguish them (optional).