Trihexes and Tetrahexes – the puzzle pieces

Trihexes are made of three regular hexagons joined along their edges; Tetrahexes are made of four.

There are three Trihexes and seven Tetrahexes. Both belong to the polyhex family.

Only three regular polygons—that is, polygons with sides of equal length and equal interior angles—can tile a plane without gaps or overlaps: the square, the equilateral triangle, and the regular hexagon.

Pentominoes are made of five squares joined along their edges, while Hexiamonds are made of six equilateral triangles. Regular hexagons can also be joined edge to edge to form shapes; these are called polyhexes.

Together, the seven Tetrahex pieces cover an area of 28 hexagons. Adding the three Trihex pieces brings the total to 37 hexagons for the complete set of ten pieces. The Tetrahex shapes gallery shows examples of shapes that can be made with the Tetrahex pieces.

The regular hexagonal grid allows shapes with up to six axes of reflection and sixfold rotational symmetry. However, the seven Tetrahex pieces cannot form a shape with this maximum symmetry. The equilateral triangle shown here cannot be made from these pieces either.

Adding the three Trihex pieces to the set makes it possible to form at least two shapes with maximum symmetry: a regular hexagon and a “snowflake.”

The 3D-printing files include the three Trihexes, the seven Tetrahexes, and a slider box.

The online Tetrahex solver runs directly in your browser—no installation or download required. You can arrange the pieces with a mouse click and then solve the resulting shape.

The solver can construct and solve shapes using either the seven Tetrahex pieces (7 × 4 = 28 hexagons) or seven Tetrahex and three Trihex pieces (7 × 4 + 3 × 3 = 37 hexagons).

The solver does not combine solutions that can be transformed into one another by rotation or reflection; they are counted separately. The interface is in English and easy to use.

The PDF contains templates in different colors for making Tetrahex pieces from cardboard.

Matching shape templates are also available.