1. © T Madas

2. What is a Polyomino?

3. © T Madas What is a Polyomino? It is a shape made up of touching squares Monomino Domino Triomino Tetromino Pentomino Hexomino Heptomino Octomino etc

4. © T Madas What is a Polyomino? It is a shape made up of touching squares Monomino Domino Triomino Tetromino Pentomino Hexomino Heptomino Octomino etc Full edge to edge contact only It can have a hole

5. © T Madas Clearly there is only 1 monomino There is only 1 domino Polyominoes produced by rotations & reflections do not count as different shapes. =

6. © T Madas Clearly there is only 1 monomino There is only 1 domino Polyominoes produced by rotations & reflections do not count as different shapes.

7. © T Madas Clearly there is only 1 monomino There is only 1 domino There are 2 triominoes There are 5 tetrominoes We need to be organised if we are to find all the pentominoes

8. © T Madas 1 2 3 4 5 6 7 8 9 10 11 12 there are 12 pentominoes

9. © T Madas

12. Which pentominoes have line symmetry? Which pentominoes have rotational symmetry and of what order? Which pentominoes could be the net of an open top cubical box? Every pentomino has an area of 5 square units but do they all have the same perimeter? The 12 pentominoes have a total area of 60 square units. By tessellating all 12 pentominoes is it possible to make up: a 6 x 10 rectangle a 5 x 12 rectangle a 4 x 15 rectangle

13. © T Madas Pentominoes with reflective symmetry

14. © T Madas Pentominoes with rotational symmetry order 2 order 4 order 2

15. © T Madas Pentominoes which fold to an open top box Shading their bases

16. © T Madas The perimeter of the pentominoes 12 10 12

17. © T Madas Fitting all the 12 pentominoes in a 6 by 10 rectangle There are 2339 different ways to fit the 12 pentominoes in a 6 by 10 rectangle. Here are 2 more ways:

18. © T Madas Fitting all the 12 pentominoes in a 5 by 12 rectangle There are 1010 different ways to fit the 12 pentominoes in a 5 by 12 rectangle. Here is another way:

19. © T Madas Fitting all the 12 pentominoes in a 4 by 15 rectangle There are 368 different ways to fit the 12 pentominoes in a 4 by 15 rectangle. Here is another way:

20. © T Madas

22. Which hexominoes have line symmetry? Which hexominoes have rotational symmetry and of what order? Which hexominoes could be the net of a cube? Every hexomino has an area of 6 square units but do they all have the same perimeter? The 35 hexominoes have a total area of 210 square units. By tessellating all 35 hexominoes is it possible to make up: a 14 x 15 rectangle a 10 x 21 rectangle a 7 x 30 rectangle a 6 x 35 rectangle

23. © T Madas Hexominoes with reflective symmetry

24. © T Madas Hexominoes with rotational symmetry order 2

25. © T Madas 11 hexominoes could be the net of a cube

26. © T Madas The perimeter of the hexominoes 14 12 14 12 10 14 12 14

27. © T Madas The 35 hexominoes have a total area of 210 units 2. By tessellating all 35 hexominoes it is NOT possible to make up any rectangle with an area of 210 units 2

28. © T Madas How many of each type of Polyomino are there? Monominoes Dominoes Triominoes Tetrominoes Pentominoes Hexominoes Heptominoes Octominoes etc         1 2 2 5 12 35 108 369 There is no formula which gives the number of all the possible n – ominoes

29. © T Madas