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 . 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.



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The problem of convex spectra was originally researched by Erich Friedman, Mike Reid, and the author of this Demonstration in 1999.
The term "convex spectrum" was introduced by Eric Friedman in 1999.
For example, the convex spectrum of a circle is {1}.
The convex spectrum of a half-circle is {1,2}.
This Demonstration considers the mathematical problem of finding all two-dimensional tiles with a finite convex spectrum.
Two interesting examples of tiles with an infinite convex spectrum are also included.
List of convex spectra displayed in this Demonstration:
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