Polyhex (mathematics)

Specific forms are named by their number of hexagons: monohex, dihex, trihex, tetrahex, etc.

Generally, however, the following rules apply: All of the polyhexes with fewer than five hexagons can form at least one regular plane tiling.

In addition, the plane tilings of the dihex and straight polyhexes are invariant under 180 degrees rotation or reflection parallel or perpendicular to the long axis of the dihex (order 2 rotational and order 4 reflection symmetry), and the hexagon tiling and some other polyhexes (like the hexahex with one hole, below) are invariant under 60, 120 or 180 degree rotation (order 6 rotational and reflection symmetry).

In addition, the hexagon is a hexiamond, so all polyhexes are also distinct polyiamonds.

They are given names, in the order shown: bar, worm, pistol, propeller, arch, bee, and wave.

A tessellation of all 7 free tetrahexes
One example self-tiling with a pentahex
With a fixed orientations, there are 3 distinct dihexes.
The smallest chiral pair are tetrahexes, like this pair. 3 of 7 are two-sided.
Polyhexes may have holes, like this hexahex.