Enhanced Sets of Octiamonds
With the octtiamonds there will be many ways to form triangles with extra copies of one of the pieces and here we look only at forming four side 12 triangles or one side 24 triangle. The first diagram shows a solution with the extra pieces placed in pairs in the first three triangles.
The following diagrams shows all solutions to forming a side 24 triangle.
Patrick Hamlyn has suggested a similar problem of packing six hexagons. Solutions for 19 of the pieces are shown here.
Patrick has found the solutions below where the extra pieces are placed one in each hexagon.