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...
12 KB (1,326 words) - 22:10, 20 July 2024
and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected...
12 KB (1,119 words) - 12:30, 29 July 2024
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...
37 KB (3,934 words) - 14:09, 15 September 2024
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...
25 KB (4,264 words) - 15:18, 17 July 2024
The Dancing Links algorithm solving a polycube puzzle...
8 KB (1,035 words) - 12:24, 10 June 2023
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...
9 KB (1,116 words) - 11:22, 20 August 2024
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...
18 KB (2,277 words) - 13:02, 27 August 2024
joined along congruent faces. Joining cubes in this way produces the polycubes, and joining tetrahedrons in this way produces the polytetrahedrons. 2-dimensional...
6 KB (391 words) - 20:17, 15 September 2024
Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study...
38 KB (4,393 words) - 06:53, 22 July 2024
Hexomino Heptomino Octomino Nonomino Decomino Higher dimensions Polyominoid Polycube Others Polyabolo Polydrafter Polyhex Polyiamond Pseudo-polyomino Polystick...
14 KB (1,641 words) - 08:17, 28 August 2024