## Tessellations

**Work Time**

# Tessellations

### Part I

If the angles that form a complete circle around a vertex are the interior angles of regular polygons, then those polygons can form the basis of a repeating pattern called a *tessellation*.

The first two images use regular polygons. This pattern is called a *regular tessellation*.

- A regular tessellation is made using six regular polygons around each point.
- What is the measure of an interior angle of that regular polygon?
- How many sides does that regular polygon have?

- A regular tessellation is made using three regular polygons around each point.
- What is the measure of an interior angle of that regular polygon?
- How many sides does that regular polygon have?

### Part 2

The second pattern is called a *semi-regular* *tessellation*, because it uses more than one type of regular polygon.

- A semi-regular tessellation is made using four regular polygons around each point.
- What is the measure of an interior angle for each regular polygon?
- How many sides does each regular polygon have?

- It is possible to arrange two regular octagons and one square around one point.
- Explain why.
- Sketch a part of the semi-regular tessellation that is produced by this arrangement.

- Work with your partner to create a list of as many regular and semi-regular tessellations as you can.