Original artwork by M. C. Escher (can you tell I have an Escher obsession?) Image source. A third type of tessellation (in addition to translations and reflections) is rotation, where instead of sliding or flipping the pattern, you spin it about a pivot point.
Step 1 - Starting again with a square, mark off the midpoint on one of the edges, and draw and cut out any pattern or squiggle you'd like, starting at either corner and going to the midpoint.
Step 2 - Give the square a quarter turn and, using the piece you just cut out as a stencil, trace and cut out the same piece from the new side, making sure you stay consistent with the first edge (i.e. if you started cutting from the left corner, don't switch to starting from the right corner). Repeat with the remaining two sides.
Step 3 - Now you should have four identical squiggly pieces cut out. On each edge of the square, there is one half that wasn't cut - position the four pieces on the uncut half as shown. If you've done it correctly, you should be able to hold the midpoint and pivot the piece about that point until it fits back into where it was cut from.
Step 4 - Tape the pieces accordingly and now your shape is ready to trace!
Can you see how this tessellation is both a rotation and a translation?
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