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/