Dissection problem

In geometry, a dissection problem is the problem of partitioning of a polytope into smaller pieces so that they may be rearranged into a different polytope of equal volume. In this context, the partitioning is called simply a dissection (of one polytope into another). Usually is is assumed that the number of the pieces of the dissection is finite.

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

External link

• David Eppstein, Dissection Tiling.