As polyominoes are shapes made joining two or more squares, polypolyominoes
(poly^{2}ominoes) are shapes made joining two or more congruent
polyominoes.

Poly^{2}ominoes are interesting when they are congruent with another
poly^{2}omino. Finding these pairs
coincidences, are sooner or later out of the reach of our computer algorithms,
so hand solvers, right now, have a chance against the machines. Anyway, only with
a computer complete search we can get the pair's smallest area shape. Some
examples:

Next links point to tables where each cell contains two congruent shapes, one is a
poly-N-omino, the other is a poly-M-omino.

Most solutions were found by Robert Reid and Michael Reid by hand, looking for the smallest possible area.

- Tetrominoes - Tromino / Domino
- Pentominoes - Pentomino / Tetromino / Tromino / Domino
- Hexomino - Tetromino / Tromino / Domino
- Hexomino - Pentomino
- Hexomino - Hexomino (in process...)
- Heptomino - Tromino / Domino
- Heptomino - Tetromino

Smallest area poly^{2}ominoes with most distinct n-ominoes.

Jorge Mireles

Last update: Nov 30 2003