Tiles with Finite Convex Spectra

Rearrange the given tiles to create convex shapes.

If copies of a tile can be arranged to form a convex shape without gaps or overlapping, then is said to belong to the "convex spectrum" of . For example, the convex spectrum of a circle is {1} and the convex spectrum of a half-circle is {1,2}. The mathematical problem is to find all shapes with finite convex spectrum.

Since the tiles and convex spectra are already given in this Demonstration, all you have to do is to rearrange the given tiles. For example, if the convex spectrum is , one task is to arrange 3 tiles into a convex shape; another task is to arrange 6 tiles into a convex shape.