hexacube

A hexacube is a three-dimensional shape composed of six unit cubes joined face-to-face. It is a type of polycube, specifically a hexacube, which is a polyomino of order 6 in three dimensions. Like other polycubes, hexacubes can be classified by their connectivity and the number of distinct shapes they can form.

There are 35 distinct free hexacubes, meaning that shapes are considered the same if they can be rotated or reflected to match each other. These 35 shapes have been enumerated and cataloged in various mathematical and computational contexts.

Hexacubes have applications in various fields, including recreational mathematics, puzzle design, and theoretical computer science. For example, certain puzzles involve assembling a given set of hexacubes into a larger structure, such as a rectangular prism. The study of polycubes, including hexacubes, is related to topics like tiling problems, packing problems, and combinatorial geometry. The enumeration of polycubes is a classic combinatorial problem that becomes increasingly complex as the number of constituent cubes increases.