The problem consists in taking two polyominoes, say a tetromino and a pentamino, and finding a figure which can be tessellated indipendently by both the polyominoes. Like these:
or 
I discovered and became interested in this problem thanks to the great
pages of
Livio Zucca (and in
particular Page1,
Page2, and
Page3)
and of Jorge
Luis Mireles which collect a large number of results, mostly
obtained by hand by a small group of polyomino "heroes".
I can't solve these problems by hand. (I have difficulties even in telling
if two polyominoes are the same apart reflection and rotation...), so
I wrote a little program that searches solutions for me, since I like to
look at them.
In the following pages I collect the results
I obtained running my little program.
I must point out that a large fraction of the solutions I report here has been probably already obtained by other people. I apologize for this, but I'm not really interested in the game of I did it before you did, nor I have the time to compare all the solutions and attribute ownership. I will do it only in the few cases in which the computer program does not find an already known solution.
I also apologize for the names of the polyominoes.
I did most of the work during the Christmas holidays, when I was out of
Internet, so I did not have a model to conform to. After that, I was too
lazy to change all the names...
A list of the polyominoes I have used is here.
The Pdf documents, in universal page format, are there to help (I hope)
the printing.
| Pairs | Web pages | Pdf documents | Solved |
| Pentomino - Tetromino | tetrominoes | tetrominoes (20Kb) | 58 / 60 |
| Pentomino - Pentomino | pentominoes | pentominoes (12Kb) | 60 / 66 |
| Hexomino - Tromino | trominoes IL | trominoes IL (13Kb) | 70 / 70 |
| Hexomino - Tetromino | tetrominoes | tetrominoes (44Kb) | 166 / 175 |
| Hexomino - Pentomino | pentominoes | pentominoes (136Kb) | 389 / 420 |
| Hexomino - Hexomino | hexominoes | hexominoes (94)k | 550 / 595 |
| Heptomino - Tromino | trominoes IL | trominoes IL (58Kb) | 216 / 216 |
| Heptomino - Tetromino | tetrominoes | tetrominoes (161Kb) | 473 / 540 |
| Heptomino - Pentomino |
Pentominoes FILN Pentominoes PTUV Pentominoes WXYZ |
Pentominoes FILN (104Kb) Pentominoes PTUV (151Kb) Pentominoes WXYZ (106Kb) |
1100 / 1296 |
| Octomino - Tromino | tromino I tromino L |
tromino I (108Kb) tromino L (97Kb) |
734 / 738 |
| Octomino - Tetromino |
tetromino I tetromino L tetromino N tetromino Q tetromino T |
tetromino I (68Kb) tetromino L (28Kb) tetromino N (63Kb) tetromino Q (48Kb) tetromino T (60Kb) |
308 / 369 369 / 369 360 / 369 144 / 369 361 / 369 |
| Octomino - Pentomino | pentominoes | Enneomino - Tetromino | tetromino I tetromino Q |
| Dekamino - Tetromino | tetromino L |
