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© 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
© 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
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
© T Madas
1 2 3
4 56 7
8
9 10 11
12 there are 12 pentominoes
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© T Madas
© T Madas
© 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
© T Madas
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
© 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:
© 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:
© T Madas
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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© T Madas
© T Madas
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
© T Madas
Hexominoes with reflective symmetry
© T Madas
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
© T Madas
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
© 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
© T Madas
© T Madas
© T Madas
© T Madas
© T Madas