Tessellation is a repeating pattern of shapes that covers a surface without gaps or overlaps. M.C. Escher was famous for his tessellation art. He used regular polygons like squares, triangles, and hexagons to tessellate. A tessellation can be created by starting with a regular polygon, drawing a line on the side, cutting it out, and translating the shape to the other side, repeating to cover the surface.

1. Tessellation
!

7. Tessellation – a
repeating pattern of
closed shapes that
covers a surface with
no gaps and no
overlaps.

8. The word tessellation comes from
the root word, tesserae, which
means tile. Many mosaic tile
installations are tessellations.

9. M.C. Escher is the
most famous
tessellation artist.
He was born in the
Netherlands in1898 and
he lived until 1972.
His father was a civil engineer who wanted his
son to be an architect.
Escher loved to draw and was fascinated by
the mathematical patterns in the world.

15. Escher knew that only a regular polygon
like the
could be tessellated.
He made his tessellations
by working with these basic shapes.
Square Triangle Hexagon

16. Translation (slide) –
A movement of a shape to a new position
along a straight line

17. Translation (slide) –
A movement of a shape to a new position
along a straight line

18. Translation (slide) –
A movement of a shape to a new position
along a straight line

19. Translation (slide) –
A movement of a shape to a new position
along a straight line

20. Reflection (flip) –
A movement of a shape to a new position by
flipping the shape over a line

21. Reflection (flip) –
A movement of a shape to a new position by
flipping the shape over a line

22. Reflection (flip) –
A movement of a shape to a new position by
flipping the shape over a line

23. Reflection (flip) –
A movement of a shape to a new position by
flipping the shape over a line

24. Rotation –
A movement of a shape to a new position by
moving the shape around a point.

25. Rotation –
A movement of a shape to a new position by
moving the shape around a point.

26. Rotation –
A movement of a shape to a new position by
moving the shape around a point.

27. Rotation –
A movement of a shape to a new position by
moving the shape around a point.

28. Rotation –
A movement of a shape to a new position by
moving the shape around a point.

29. Transformation –
The movement of a shape by translation,
reflection or rotation

30. Transformation –
The movement of a shape by translation,
reflection or rotation

31. Transformation –
The movement of a shape by translation,
reflection or rotation.

32. Transformation –
The movement of a shape by translation,
reflection or rotation

33. Transformation –
The movement of a shape by translation,
reflection or rotation

34. Now, let’s discover
how to make
your own
tessellating shape!

35. Start with a regular polygon, like a square
(it could also be a triangle, hexagon, or octagon)

36. Start with a regular polygon, like a square.
Draw a line on the side of the square.

37. Start with a regular polygon, like a square.
Draw a line on the side of the square.
Then cut out the shape, translate and tape the
shape to the other side of the square.

38. Here is your tessellating shape.

39. Now it is time to imagine what
you have created.
Maybe it’s a fish

40. Now it is time to imagine
what you have created.
The fish becomes a school of fish!

41. Now imagine another idea with the same
tessellating shape.
Maybe it’s a ….!

42. Now imagine another idea with the same
tessellating shape.
Maybe it’s a ….!

43. Now imagine another idea with the same
tessellating shape.
Maybe it’s a ….!

44. Now imagine another idea with the same
tessellating shape.
Maybe it’s a Kitten!

45. Which becomes a whole litter of kittens!

47. Let’s
Tessellate!

48. Now it is time to make your
own tessellating shape.
Remember, you can make a
transformation by translating,
reflecting, or rotating your shape.

49. Decide what your shape can be.
Add details to it, repeating them
in all the shapes you trace.
Add color to make your
tessellation come to life.
Repeating color patterns
look best.