Dissection problem

In geometry, dissection is the partitioning of a polytope into smaller pieces so that they may be rearranged into a different polytope of equal volume.

This process can be performed on any polygon to yield any other polygon of equal area. For that, see Bolyai-Gerwien theorem. 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

• Shape dissection
• Scissors congruence, Hilbert's third problem

External link

• David Eppstein, Dissection Tiling.