tessellation

3.1 Create a Tessellation
We adore chaos because we love to produce order.
—M. C. Escher (1898–1972)

Directions for creating a tessellation based on a parallelogram. (You may want to use Geometer's Sketchpad for the construction.)

(1) Construct a parallelogram.
(2) Construct a figure along one edge of the parallelogram.
(3) Translate the figure to the opposite side of the parallelogram.
(4) Construct a shape along one of the other sides of the parallelogram.
(5) Translate the shape to the opposite side of the parallelogram.
(6) Hide the original parallelogram.
(7) Create the tessellation by translating the figure.
(8) Color the interiors as desired.

Diagram illustrating the steps to a construction of a tessellation. Final step in the tessellation construction. Completed tessellation with color.

What other basic shapes besides a parallelogram may be used to construct a tessellation?

3.1.1 Introduction to Transformational Geometry