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...

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...

The Dancing Links algorithm solving a polycube puzzle...

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...

 A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS...

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...

examples. Squares: The cube is the only convex example. Other examples (the polycubes) can be obtained by joining cubes together, although care must be taken...

(ed.). "Sequence A000162 (Number of three dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS...

Hexomino Heptomino Octomino Nonomino Decomino Higher dimensions Polyominoid Polycube Others Polyabolo Polydrafter Polyhex Polyiamond Pseudo-polyomino Polystick...

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...

52 + 72 + 112 + 132 + 172 + 192. It is the number of three-dimensional polycubes with seven cells. 1023 is the number of elements in the 9-simplex, as...

primes (193 + 197 + 199 + 211 + 223); the number of three-dimensional polycubes with 7 cells; number of elements in a 9-simplex; highest number one can...

of scientific advances in fields as diverse as musical similarity,[MMS] polycube unfolding,[CUP] computational archaeology,[WBT] and protein folding. Langerman's...

Iljasov on 25 February 2008. Slothouber–Graatsma puzzle Conway puzzle Polycube Soma cube [1] Archived 2008-05-09 at the Wayback Machine: "Bruce Bedlam...

Fibonacci(n)!. Mar 14, 2001 A066288 Number of 3-dimensional polyominoes (or polycubes) with n cells and symmetry group of order exactly 24. Jan 1, 2002 A075000...

how it can be used to solve puzzles 1972 Sep Pleasurable problems with polycubes, and the winning strategy for Slither 1972 Oct Why the long arm of coincidence...

diabolical cube is a three-dimensional dissection puzzle consisting of six polycubes (shapes formed by gluing cubes together face to face) that can be assembled...

mesh to conform to the input; see Automatic Hex-Mesh Generation based on polycube. Another direct method is to cut the structured cells by the domain boundary;...

disjoint tripods in a three-dimensional grid, where a tripod is an infinite polycube, the union of the grid cubes along three positive axis-aligned rays with...

contemporary artists". The Art Directors of Philadelphia awarded him the Polycube Award for "consistent excellence in communications". The City of Milan...

also produced hands-on teaching materials including workbooks for the polycube. He also drew upon insights into pedagogy in the writings of Mary Boole...

the tripod packing problem. The tripods of this problem are infinite polycubes, the unions of the lattice cubes along three axis-parallel rays, and they...

analogue of a polyiamond. Polytetrahedra and polyiamonds are related as polycubes are related to polyominoes. In origami, a polypolyhedron is "a compound...

rectangular cuboid. The Herzberger Quader consists of a set of all possible polycubes from dicube to tetracubes. The eleven pieces together have 40 unit cubes...

Slothouber–Graatsma puzzle is an example of a cube-packing puzzle using convex polycubes. More general puzzles involving the packing of convex rectangular blocks...

chapters concern lattice tilings by polycubes. The question here is to determine, from the shape of the polycube, whether all cubes in the tiling meet...

chapters of the first edition concern generalizations of polyominoes to polycubes and other polyforms, and briefly mention the work of Edward F. Moore and...