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A pentomino is a polyomino of order 5, meaning it is composed of five congruent squares, connected edge to edge. There are 12 distinct free pentominoes, often denoted by letters that they resemble: F, I, L, P, N, T, U, V, W, X, Y, and Z. The "free" classification means that rotations and reflections of a shape are considered the same pentomino. If reflections are considered distinct, then there are 18 one-sided pentominoes.

Pentominoes are commonly used in recreational mathematics, particularly in tiling puzzles. The goal of many pentomino puzzles is to tile a given rectangular area or a specific shape using a subset or all of the 12 pentominoes. For example, a classic puzzle involves tiling a 6x10 rectangle using all 12 pentominoes. This is possible, and there are 2339 distinct solutions. Other puzzles might involve tiling smaller rectangles, such as 3x20 or 4x15, also using all 12 pentominoes.

The study of pentominoes and their tiling properties has connections to combinatorics and computational geometry. Determining whether a given region can be tiled by a specific set of pentominoes can be a complex problem. The number of ways to tile a shape with pentominoes is a subject of ongoing research and has led to the development of algorithms for solving such tiling problems.