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What is a Polyomino?
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What is a Polyomino?
•Monomino
•Domino
•Triomino
•Tetromino
•Pentomino
•Hexomino
•Heptomino
•Octomino
etc
It is a shape made up
of touching squares
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What is a Polyomino?
It can have a hole
It is a shape made up
of touching squares
•Monomino
•Domino
•Triomino
•Tetromino
•Pentomino
•Hexomino
•Heptomino
•Octomino
etc
Full edge to edge
contact only
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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.
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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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3
2
1
4
5
7
6
8
9
12
10
11
there are 12 pentominoes
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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
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Pentominoes with reflective symmetry
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Pentominoes with rotational symmetry
order 2
order 4
order 2
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Pentominoes which fold to an open top box
Shading their bases
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The perimeter of the pentominoes
12
12
12
10
12
12
12
12
12
12
12
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 rectangle
There 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 rectangle
a 10 x 21 rectangle
a 7 x 30 rectangle
a 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
14
14
14
12
14
14
14
14
14
14
12
14
14
12
14
12
10
14
14
14
14
14
14
12
14
12
14
14
12
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 a 1
•Dominoes
a 2
•Triominoes a 2
•Tetrominoes a 5
•Pentominoes a 12
•Hexominoes a 35
•Heptominoes a 108
•Octominoes a 369
etc
There is no formula which
gives the number of all the
possible n – ominoes
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