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### Polyominoes

```
Date: 09/08/97 at 00:20:03
From: John
Subject: Shapes

I am using polyominos, but I do not know how to tell my dad what they
are.  How can I tell him so he will know?
```

```
Date: 09/08/97 at 02:16:21
From: Doctor Sarah
Subject: Re: Shapes

Hi John -

Polyominoes are shapes formed by connecting equal-sized squares, each
joined together with at least one other square along an edge. The
shape of a polyomino can grow quite complex when there are many
squares.

A domino has two squares. Then come

trominoes   (3 squares)
tetrominoes (4)
pentominoes (5)
hexominoes  (6)
heptominoes (7)

The 5 tetrominoes:

xx      xx      x        x
xx     xx     xxx     xxx     xxxx

The 12 pentominoes:

xx    x      x      x    x            x
xx   xxx   xxx   xxx   xxx   xxx     x   x x   xx       x       x   xxxxx
x     x     x     x    x     xx   xxx   xxx    xxx   xxxx   xxxx

The 35 hexominoes:

xxx    xx     x       x       x       x    x      x    x       x    xxx
xx    xxx   xxxx   xxxx   xxxx   xxxx   xxx   xxx   xxxx   xxxx     x
x      x      x      x      x      x   x x   x x     x      x      xx

xx      x       x           xx     x      x    x                    xx
xx    xxx    xxx    xxxx    xx   xxx   xxx   xx     xxx     xxx     x
xx     xx     xx     xx    xx    xx    xx    xxx     xxx    xxx   xxx

x           x              x
xx x    xx   xxx     x     xx       x   x  x    x x     xx     x        x
xxx   xxx   xxx   xxxx   xxxx   xxxx   xxxx   xxxx   xxxx   xxxxx   xxxxx

x
xxxxx   xxxxxx

The 108 heptominoes:

xxx      xx       x         x         x      xx       x         x         x
xx      xxx     xxxx     xxxx     xxxx      xx      xxx      xxx      xxx
x        x        x        x        x       xx       xx       xx       xx
x        x        x        x        x        x        x        x        x

xx        x                                     x         x
xxxx       x       xx       xxx       xxx      xx         x         x
xx      xxx      xxx       xxx      xxx      xxxx     xxxx     xxxx
x        x        x         x        x         x        x        x

x
x x       xx         x     x          x          x          x          x
xxxx     xxxx     xxxx     xxxxx     xxxxx     xxxxx     xxxxx     xxxxx
x        x        x         x         x         x         x         x

x         x     xx       x x      x         x         x      x         x
xxxx     xxxx      xxx     xxx     xxxx     xxxx     xxxx      xxx      xxx
x  x     x  x      x x     x x      x x      x x      x x     xx x     xx x

x        x        x
x     xxx     xxx        x       x          x          x       x
xxx       xx      xx     xxxx     xxxxx     xxxxx     xxxxx    xxxxx
xx x       x       x        x         x         x         x       x

xxxx     xxx      xxx     xx        xx        xx      x         x         x
x       xx      xx      xxx     xxx      xxx      xxxx     xxxx     xxxx
xx       xx      xx      xx       xx       xx        xx       xx       xx

xxx      xx       xx      x x      xx     x         x
xxxxx       xxx        xx      xxx     xxx     xxx     xxx     xxxx     xxxx
xx     xx xx       xx       xx      xx      xx      xx       xx       xx

x         x       x      xxx        xx       x          x
xxxx     xxxx     xxxx       x       xx       xxx       xxx       xxxx
xx       xx      xx        xxx      xxx       xxx       xxx        xxx

xxx       x         x                xxx     xx        xx     x         x
x      xxx      xxx      xxxx        x      x x     x x     xx x     xx x
xxx      xxx      xxx       xxx     xxx      xxx     xxx      xxx      xxx

x                 xx      x         xx        xx                 x
xx x     xxx x       xx     xx          x        x      xx x       xx
xxx       xxx      xxx      xxxx     xxxx     xxxx      xxxx     xxxx

x
x       xx        x                x          x       x         x
x        x     x  x     xx  x      x x      x x       xx       xx     x xx
xxxx     xxxx     xxxx      xxxx     xxxx     xxxx     xxxx     xxxx     xxxx

x          x                              x
xxx       x          x       x x        xx          x     x   x      x  x
xxxx     xxxxx     xxxxx     xxxxx     xxxxx     xxxxx     xxxxx     xxxxx

x x        xx        x           x           x
xxxxx     xxxxx     xxxxxx     xxxxxx     xxxxxx     xxxxxxx

-Doctor Sarah,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Definitions
High School Euclidean/Plane Geometry
High School Geometry
High School Triangles and Other Polygons
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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