Brendan Owen has suggested forming figures from the combination of pairs of hexagons. The following table is due to him.
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The figure below shows the six didohexes and the nine one-sided didohexes.
There are 74 tridohexes shown here in a number of constructions.
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).