2. TESSELLATIONS

3. What’s a tessellation? Tessellations are a series of repeating patterns or designs that interlock. The positive and negative space work together to create the images. The pattern must include not only objects but the spaces between them

4. Where have you seen them?

5. 2 Main Types of Tessellations Regular Semi-regular

6. REGULAR TESSELLATIONS RULE #1: The tessellation must tile a floor (that goes on forever) with no overlapping or gaps.  RULE #2: The tiles must be regular polygons - and all the same.  RULE #3: Each vertex must look the same.

7. where all the "corners" meet! What can we tessellate using these rules? Triangles? Yep! Notice what happens at each vertex! What’s a vertex?

8. Squares? Yep!Will pentagons work? Nope! Hexagons? Yep! Heptagons? No way!! Now we are getting overlaps! Octagons? Nope! - They'll overlap too. In fact, all polygons with more than six sides will overlap! So, the only regular polygons that tessellate are triangles, squares and hexagons!

9. SEMI-REGULAR TESSELLATIONS These tessellations are made by using two or more different regular polygons. The rules are still the same. Every vertex must have the exact same configuration.

10. Examples

11. Quick Quiz What is another name for tessellation? What is the difference between a regular and semi-regular tessellation? Name a polygon used in regular tessellation? Complete the sentence: In a tessellation, every vertex must _____.

12. Tessellation in Art

13. M. C. Escher

15. Make your own tessellation There are two shapes that you can make Both start with a square of posterboard

16. Shape 1 Cut a shape form one side of a tile, tape it on the opposite side directly across from the cut out.

17. Shape 1 Cut the shape in half, then tape them opposite each other. This is your tessellating shape!

18. Shape 2 Cut a square tile in half in the desired shape and tape one side to the other.

19. Shape 2 Cut the newly made shape in half again in the desired way. Take the top two pieces and move them below the bottom two pieces. Align and tape with the corners matching. This is your tessellating shape!

20. Use your imagination!

21. HAVE FUN!

22. Make Your Own Tessellation Shape 1. Start with a square. Cut a shape form one side of a tile, tape it on the opposite side directly across from the cut out. Cut the shape in half, then tape them opposite each other. This is your tessellating shape! Shape 2. Cut a square tile in half in the desired shape and tape one side to the other. Cut the newly made shape in half again in the desired way. Take the top two pieces and move them below the bottom two pieces. Align and tape with the corners matching. This is your tessellating shape!