Polyominoes

2025/8/31

Polyominoes are the shapes made of squares that are all the same size and connected by their edges and corners. This project generates all of them in a specific way/order. It checks each existing polyomino and checks every spot to add one new square without creating duplicate shapes. After generation, colors are used for the eight symmetry groups polyominoes can have.

To clarify, these are free polyominoes. One-sided ones have their two different flipped versions counting as distinct shapes. Fixed ones have all eight of their flips and rotations considered different shapes.

There's also another mode where you can see that every fixed polyomino corresponds to two max-symmetry free  polyominoes.

• Z: Previous
• X: Next
• R: Random
• Q: Enter polyomino number
• P: Restart project

Hold shift while pressing Z or X to go to another polyomino with the same symmetry.