Laboratory Investigation 11.2Tessellations
The following steps illustrate a method of altering the sides of an equilateral
triangle to obtain a non polygonal figure that will tessellate. These steps can
be carried out with pencil and paper or by computer software programs.
Step 1 Draw a curve from A to B.

Once the lines of the original figure have been erased, the figure that remains
will tessellate.
Starting Points for Investigations

If the preceding figure is used to form a tessellation, which of the
transformations (rotation, translation, reflection) will map the preceding
tessellation onto itself?

Step 3 produces a curve on one side of the triangle that is said to have
point symmetry because it can be rotated onto itself by a 180˚ rotation.
Suppose Step 3 is used to produce a curve with point symmetry on all three
sides of a triangle. Will the resulting figure tessellate?

Suppose Step 3 is used to create a curve with point symmetry on each of
the six sides of a regular hexagon. Will the resulting figure tessellate?