**About Sextuplets**

Sextuplets are shapes
consisting of 25 unit hexes, six copies of which can be
tiled using a complete set of mono- through pentahexes. In
order to restrict the number of possible shapes, the
majority of solutions posted here display some sort of
symmetry. All solutions with horizontal mirror symmetry may
be connected in at least one way, to form a single 150-unit
shape with full symmetry. Unfortunately, the same does not
apply to solutions with vertical mirror symmetry, as shown
below.

However, it is possible
to form a 24-unit vertically symmetric shape adding the
final hex along one of the axes shown in pink. These
"offset" shapes can now construct a fully symmetric figure.
The same procedure can be applied to a horizontally
symmetric

generator, but there are now two
possible starting positions on the grid.

**Related Solutions**

Each birotary shape is
related to three horizontally and three vertically symmetric
shapes as shown below. In this case the central shape on the
bottom row also possesses ternary symmetry. The resulting 25
hex shapes cannot necessarily be solved as sextuplets.