With 24 pieces it might be possible to produce three, four or six congruent shapes with a full set. All of these are possible as shown in the following diagrams by Pieter Torbijn.

Pieter Torbijn has also solved a number of other heptiamond problems as shown below.

1. Join 6 heptiamonds and then extend the construction to make a shape similar to the original but twice the size.

2. Create a shape which contains one (or more) holes similar in shape to the original.