Inspired by an entry
regarding polyomino variations in the
Puzzle Zapper blog, by
Alexandre Muņiz, I decided to look at the same phenomenon
for the polyhexes. A hexagon has 12 symmetries - 6 rotations
and 6 reflections. By restricting these symmetries, we can
create derivative sets of pieces with different properties.
The diagrams below show the possible positions of a red
"peg" starting at the top-left. Physical pieces could be
made in this way, with holes drilled at the positions of any
red circles, and pegs set at the upper-left of each hex on
the board. Pieces can also be made by adding a suitably
shaped single hole, which must be aligned the same way in
any solution, or by varying the geometry of the edges. These
pieces can be made to completely tile the plane, with the
exception of pieces with ternary and vertical symmetry,
which require holes, gaps or a surface design.

**
**
Symmetry-Restricted Hexagons