Tetrahex – Pentoma Puzzles

Tri- and Tetrahex pieces

By combining three regular hexagons, you obtain trihexes. The tetrahexes consist of four connected hexagons.

There are three trihexes and seven tetrahexes. They belong to the family of polyhexes.

Puzzles made from Trihexes and Tetrahexes

There are exactly three regular polygons – that is, polygons with equal side lengths and equal interior angles – that can tile a plane, meaning they can cover it completely without gaps or overlaps: the square, the equilateral triangle, and the regular hexagon.

Just as pentominoes were derived from the square and hexiamonds from the equilateral triangle, it was natural to develop a corresponding puzzle from regular hexagons as well: a puzzle made from so-called polyhives.

The seven tetrahex pieces together form an area of 28 hexagons. When supplemented by the three trihex pieces, the result is 37 cells for a complete set of ten pieces. On the Tetrahex shape page, you can find several examples of shapes that can be formed using the tetrahexes.

The underlying honeycomb grid allows for six axes of reflection and six axes of rotation (that is, maximal symmetry). However, if you restrict yourself to the seven tetrahexes, there is no shape with maximal symmetry – even an equilateral triangle (as shown) cannot be formed with them.

If you extend the set by adding the three trihex pieces, at least two shapes with maximal symmetry exist: a hexagon and a “snowflake.” These are presumably the only shapes with this property.