Polyhexes are the hexagon version of polyominoes.
Polyominoes are the shapes you can make by joining squares by their sides - for instance a domino is a polyomino made from just 2 squares.
With polyhexes you join regular hexagons by their sides.
(the following catalogue omits mirror images)
With a single hexagon there is of course just one variant, which tessellates:
With two hexagons there is again just one variant, which tessellates (in many ways, of which one is shown):
There are 3 ways to arrange 3 hexagons; all tessellate, as shown in the (non-unique) examples here:
There are 7 ways to arrange 4 hexagons, which again all tessellate:
There are 22 ways to arrange 5 hexagons, which also tessellate:
There are 82 ways to arrange 6 hexagons, 333 ways to arrange 7... The sequence is in Sloane's catalogue of integer sequences..
page date: 5Mar04. I enjoy correspondence stimulated by this site. You can contact me here.