Equidecomposable is a mathematical term that refers to two or more shapes that can be divided into smaller pieces that can then be assembled to form identical shapes. Other words with similar meaning to equidecomposable include equicomposable, tileable, and dissectable. Additionally, they can be referred to as congruent, as they share the same shape and size, or equivariant, meaning they can be altered in such a way that preserves their symmetrical features. Equidecomposable shapes are essential in various fields of mathematics, particularly in topology and geometric measure theory. They are also frequently used in computational geometry to achieve optimal packing solutions.