Brendan Owen has suggested forming figures from the combination of pairs of hexagons. The following table is due to him.
The figure below shows the six didohexes and the nine one-sided didohexes.
The diagram below shows two constructions made with the 73 tridohexes without a hole.
There are 134 one-sided tridohexes including one with a hole. The pieces without a hole can form seven 6x19 parallelograms.
Pairs of congruent figures are also possible with the set.
Brendan Owen has found a set of 19 congruent shapes made with this set (omitting the piece with a hole).