A polycube is a solid figure formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes...

and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected...

constructed with six square pyramids, tiling space by attaching their apices. Polycube is a polyhedron in which the faces of many cubes are attached. Analogously...

Unlike in three dimensions in which distances between vertices of a polycube with unit edges excludes √7 due to Legendre's three-square theorem, Lagrange's...

240 possible solutions by hand in 1961. The seven Soma pieces are six polycubes of order four, and one of order three: Piet Hein authorized a finely crafted...

joined along congruent faces. Joining cubes in this way produces the polycubes, and joining tetrahedrons in this way produces the polytetrahedrons. 2-dimensional...

The Dancing Links algorithm solving a polycube puzzle...

sets, each of which consists only of a single rectangle. A pentacube is a polycube of five cubes. Of the 29 pentacubes, exactly twelve pentacubes are flat...

perspective is that of looking down into a three-dimensional rectangular pit. Polycube blocks of various shapes appear, one at a time, and fall slowly toward...

Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study...