If we add a half hexagon to a trihex we get thirty-two pieces seen here making a number of sets of two and one set of four congruent shapes.

The one-sided set consists of 61 pieces.

Adding three hexagons to a half hexagon gives us a set of 36 pieces (four more than the above).

A number of sliced parallelograms are also possible with the set.

The one-sided set consists of 69 pieces.

A large number of slice parallelograms are possible with this set.