© T Madas. What is a Polyomino? © T Madas What is a Polyomino? It is a shape made up of touching...

© T Madas

© T Madas

What is a Polyomino?

© T Madas

What is a Polyomino?

It is a shape made up of touching squares

•Monomino•Domino•Triomino•Tetromino•Pentomino•Hexomino•Heptomino•Octomino etc

© 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

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Clearly there is only 1 monomino

There is only 1 domino

Polyominoes produced by rotations & reflections do not count as different shapes.

=

© T Madas

Clearly there is only 1 monomino

There is only 1 domino

Polyominoes produced by rotations & reflections do not count as different shapes.

© 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

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1 2 3

4 56 7

8

9 10 11

12 there are 12 pentominoes

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© T Madas

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 rectanglea 5 x 12 rectanglea 4 x 15 rectangle

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Pentominoes with reflective symmetry

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Pentominoes with rotational symmetry

order 2

order 4order 2

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Pentominoes which fold to an open top boxShading their bases

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The perimeter of the pentominoes

12 12 12 12

10 1212 12

12 1212

12

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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:

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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:

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Fitting all the 12 pentominoes in a 4 by 15 rectangleThere are 368 different ways to fit the 12 pentominoes in a 4 by 15 rectangle.

Here is another way:

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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 rectanglea 10 x 21 rectanglea 7 x 30 rectanglea 6 x 35 rectangle

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Hexominoes with reflective symmetry

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Hexominoes with rotational symmetry

order 2

order 2

order 2 order 2 order 2

order 2

order 2

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11 hexominoes could be the net of a cube

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The perimeter of the hexominoes

14 14 14 14 14

12 12

14 1414 14

14 14 14

14 14 14 14

12 10 14

14 14 14

1414

1212

12

12 14

14 1414

14

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The 35 hexominoes have a total area of 210 units2.

By tessellating all 35 hexominoes it is NOT possible to make up any rectangle with an

area of 210 units2

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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

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