Dissection problem

In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces.

The Bolyai-Gerwien theorem states that any polygon may be dissected into any other polygon of the same area. It is not true, however, that any polyhedron has a dissection into any other polyhedron of the same volume. This process is possible, however, for any two zonohedra of equal volume.

See also

• Dissection puzzle
• Scissors congruence
• Hilbert's third problem

External links

• David Eppstein, Dissection Tiling.