The document discusses tessellations, which are shapes that can cover a surface without gaps by repeating copies of the shape. Common shapes like squares and triangles can tessellate, but unusual shapes or combinations of different shapes may also tessellate. Specific tessellation shapes are discussed, including pentominoes (shapes made of 5 connected squares) and 7-pin polygons. Instructions are provided for creating original tessellations by modifying basic shapes that tessellate.

1. Tessellation

2. Tessellation If many copies of a shape can be used to cover a surface, without leaving any gaps between them, then we say that the shape will tessellate . The pattern that is formed is called a tessellation.

3. Tessellations all around us Look for tessellations in walls, patios and pavements.

4. Tessellations all around us Common shapes can be arranged in unusual ways Sometimes an unusual shape will tessellate

5. Tessellations all around us Sometimes 2 or more different shapes will tessellate.

6. Tessellation with Pentominoes If you don’t know what a pentomino is, then click here. If you have done the pentominoes activity before, then you will know what a pentomino is and how many different pentominoes there are. Here they are ...

7. Tessellation with Pentominoes Which Pentominoes will tessellate? Here is one example to get you started….

8. Tessellation with Pentominoes

9. Tessellation with 7-Pin Polygons If you don’t know what a 7-pin polygon is, then click here. If you have done the 7-pin polygons activity before, then you will know what a 7-pin polygon is and how many different ones there are. Here they are ...

10. Tessellation with 7-Pin Polygons Which 7-pin polygons will tessellate? Here is one example to get you started….

11. Tessellation with 7-Pin Polygons

12. Tessellations by M.C. Escher

13. Make Your Own Escher Tessellations 1 Step 1: Start with a simple shape that will tessellate e.g. a rectangle. Step 2: Remove a shape or shapes from one side of the rectangle and fix them to the opposite side.

14. Make Your Own Escher Tessellations 1 Use this as a template to create your tessellation.

15. Make Your Own Escher Tessellations 2 You could start with a hexagon and cut semi-circles from three of the sides and fix them to the opposite sides like this.

16. Make Your Own Escher Tessellations 2

17. Make Your Own Escher Tessellations 3 Start with a square and cut segments from two sides and fix them to the opposite sides like this.

18. Make Your Own Escher Tessellations 3

19. Enjoy making your own tessellations!

20. Pentominoes A pentomino is made out of five squares that are connected along at least one edge. These are NOT pentominoes. Here is an example of a pentomino. How many different pentominoes can you find? Click here to return to the Tessellations.

21. 7-Pin Polygons Here is an arrangement of 7 pins. Here are some examples of 7-pin polygons. How many different 7-pin polygons can you find? Click here to return to the Tessellations. A 7-pin polygon is a closed shape with straight sides with corners on the pins.

22. Enjoy making your own tessellations!