Enhanced Sets of Heptiamonds
With the heptiamonds there will be many ways to form paralleograms with extra copies of one of the pieces and here we look only at forming triangles. If we added four extra copies of a piece then a side fourteen triangle can be made in all 24 cases.
Larger triangles (sides 21 and 28) are possible with at least one of the pieces. The lower diagram shows a side 35 triangle.
Patrick Hamlyn has found six more examples of side 21 triangles.