Polyhexes

Polyhexes are figures built from congruent unit-length hexagons. We represent a hexagon forming a polyhex simply by a pair corresponding to the complex coordinates of its left-bottom corner . For this reason, all the corresponding functions turn out to be straightforward adaptations of their polyiamond counterparts.

The neighbors of a hexagon are , , , , , and . Thus, we can simulate a hexagonal cellular space by a rectangular cellular space in which the neighbors are these nonadjacent ones. The following function generates all polyhexes of a given order.

The number of different polyhexes is given by the following table ([5, 6], seq. A000228).