Welcome to the Labyrinth.

This site is a encyclopedia and shrine to the polyominoes, figures made of squares joined by their edges:

Underlying their simple definition are complex and intricate shapes whose properties are still not fully known. There is no known formula for counting the number of polyominoes of a given size, and the ways that polyominoes tile and fit together are still being explored.

Polyominoes have been featured in video games such as Tetris, to board games such as Blokus and Patchwork, to pencil puzzles such as Fillomino.

This site documents several interesting properties of polyominoes:

Catalog

A list of polyominoes up to octominoes with a summary of their properties.

Symmetry

An explanation of the different types of symmetries a polyomino can have.

Classes

A hierarchial categorization of polyominoes based on "directedness".

Packing

Fitting a set of polyominoes tightly in some container.

Tiling

Whether a single polyomino can completely fill the plane.

Genealogy

A "family tree" showing how polyominoes are built from simpler polyominoes.

This site is still a work in progress, and the world of polyominoes extends far beyond. So please, enjoy, learn, and get lost in the labyrinth.

And please, watch out for the mino-taur.