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).
Additionally, to avoid set-theoretic issues related to the Banach–Tarski paradox and Tarski's circle-squaring problem, the pieces are typically required to be well-behaved.
For instance, they may be restricted to being the closures of disjoint open sets.
A partition into triangles of equal area is called an equidissection.