Solomon W. Golomb was the first to study pentominoes systematically. He defined them as plane figures composed of five congruent squares, each square sharing at least one full side with another.

Since there are exactly twelve possible combinations – disregarding symmetrical duplicates – there exist twelve distinct pentominoes. Golomb assigned them letters as names, which I also use on this website. Pentominoes are two-dimensional objects and belong to the family of polyominoes.

When cubes are used instead of squares, three-dimensional solids such as cuboids can be constructed. These three-dimensional pentominoes are discussed on the page Pentomino 3D.

Where to Get Pentominoes

Pentomino sets are available commercially, but they can also be easily crafted from cardboard or produced with a 3D printer. The purchased version shown here, as well as the 3D-printable version available in the download section, even allow for three-dimensional play.

Twelve pentominoes together cover an area of 60 squares. To fill a game board of 8 × 8 units, commercially available sets (such as the one shown here) often include one additional piece.

Shapes and Solving Programs

There is a wide variety of possible shapes for the Pentomino puzzle. A selection of them can be found on the Shape Overview page.

The shape templates offered in the download section are suitable for both handcrafted cardboard and 3D-printed pentominoes.

With the solving program available on this website, even checkerboard-patterned pentomino figures can be solved. In addition, free software such as Puzzlesolver and burrTools allows you to create your own shapes or complete sets made from pentomino pieces.

If the squares of the pentomino pieces are alternately colored light and dark, a checkerboard pattern emerges. This greatly reduces the number of possible solutions for each shape and makes the puzzle significantly more challenging.

For each pentomino piece, there are two possible ways to apply such a checkerboard pattern. Accordingly, many different sets of checkerboard pentominoes exist. The crafting templates available in the download section also include a version with a checkerboard pattern.

Three different boxes are available:
The 3×4×5 box uses the 12 pentominoes. This puzzle is the most difficult, even though it offers 3,940 different solutions.
The 1×8×8 box includes the O-tetromino in addition to the 12 pentominoes.

The solving program for the two-dimensional pentominoes is part of a software collection available for download on Itch.io. It is for Windows only.

IMPORTANT: For a correct installation, please read the Instructions before unpacking!

Download multicolored crafting templates and a crafting guide for a cardboard pentomino puzzle

Shape templates matching the crafting templates