Original artwork by M. C. Escher. Image source. In addition to translations, another type of tessellation is a reflection, where a shape has been flipped about either the x or y axis.
Step 1 - Like for translations, start with a square piece of paper. Now pick one edge, mark off the midpoint, and draw some kind of squiggle from the corner to the center point.
Step 2 - Cut out the piece you've just drawn, flip it over, and line it up with the other half of the chosen edge. Trace and cut out. Now you'll have two little pieces that are reflections of each other.
Step 3 - Take those two pieces and line them up on the opposite edge as shown. Trace and cut out.
Step 4 - Attach the four pieces you've cut out to the two uncut edges like so. If you've done this correctly, you'll be able to draw a line right down the middle both horizontally and vertically and have the two sides be mirror images of one another.
Now your beautiful stencil is ready to trace!
Notice how, because of the symmetry, it doesn't matter which side is facing up.
This pattern also has some neat rotational symmetry, but that's another story...
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