1. What is a tessellation, and how are transformations used to create a tessellation?

2. Which regular polygons tessellate? (List all.)

3. Consider your answer to Question 2. Why do these regular polygons tessellate while other regular polygons do not? Include a discussion of interior angles in your response. Also include an example of a regular polygon that would not tessellate and explain why it would not.

4. Using your geometry software, create a regular tessellation. You may use color patterns to make the tessellation more visually interesting. Make a screenshot of your tessellation and paste it into this assignment.

In the space provided below, write a detailed explanation of the steps you followed to create your tessellation. A model worksheet and response have been provided for you. If you choose to tessellate the same regular polygon as the example provided, you must use different transformations from those used in the model.

1. A tessellation is a repeated pattern of shapes such as polygons with no or little space between them. To create the pattern, the shape or polygon being tessellated is transformed by rotating (rotation), sliding (translation), reflecting (reflection) or occasionally enlarging or reducing in size (dilation).

2. Equilateral triangles, squares and regular polygons.

3. Their interior angles when tessellated form 360 degrees which forms a closed gap tessellation.

4. Create a tessellation by choosing a regular polygon and creating a pattern with it solely by turning, flipping, and sliding it. You can also take a regular polygon and manipulate it to make original shapes. The artist M. C. is a great example of this.

Step-by-step explanation:

Tessellations is a centuries old technique for pattern making visible most commonly in mosaics. A tessellation is a repeated pattern of shapes such as polygons with no or little space between them. To create the pattern, the shape or polygon being tessellated is transformed by rotating (rotation), sliding (translation), reflecting (reflection) or occasionally enlarging or reducing in size (dilation). It is important that no gap is present unless in the real world where grout is needed to hold pieces together.

Because tessellations have no gap, the interior angles of the the selected shape will align and form 360 degrees. Since regular polygons are shapes which have equal sides and equal angles, only squares, equilateral triangles and a regular hexagon will add to 360 when placed together and tessellate.

See attached example and non-example.