Heptahexes
There are 333 heptahexes including two with holes shown here in three and nine congruent shapes.
The construction below was made by Peter Esser.
The 331 pieces without a hole can form a 7x331 'parallelogram'.
There are 620 one-sided heptahexes and Peter Esser has found ten congruent 'rectangles' with the set. The first four constructions use only asymmetric pieces and so can be reflected to get the remaining four parts.
Another construction by Peter is of six hexagons with the 618 pieces without a hole. The first two hexagons can be reflected to form the two remaining ones.
Twenty and thirty-one congruent shapes can also be made from the set. It is not known if 62 congruent shapes can be made.
