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...
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and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected...
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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...
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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...
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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...
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The Dancing Links algorithm solving a polycube puzzle...
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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...
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joined along congruent faces. Joining cubes in this way produces the polycubes, and joining tetrahedrons in this way produces the polytetrahedrons. 2-dimensional...
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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...
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Iljasov on 25 February 2008. Slothouber–Graatsma puzzle Conway puzzle Polycube Soma cube [1] Archived 2008-05-09 at the Wayback Machine: "Bruce Bedlam...
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Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study...
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for example, unfolding the surface of a polyhedron to a polygonal net. Polycubes are a special case of orthogonal polyhedra that can be decomposed into...
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Hexomino Heptomino Octomino Nonomino Decomino Higher dimensions Polyominoid Polycube Others Polyabolo Polydrafter Polyhex Polyiamond Pseudo-polyomino Polystick...
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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...
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(ed.). "Sequence A000162 (Number of three dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS...
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Common net (section Polycubes)
polyhedra. *Non-orthogonal foldings The first cases of common nets of polycubes found was the work by George Miller, with a later contribution of Donald...
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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...
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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...
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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;...
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also produced hands-on teaching materials including workbooks for the polycube. He also drew upon insights into pedagogy in the writings of Mary Boole...
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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...
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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...
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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...
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analogue of a polyiamond. Polytetrahedra and polyiamonds are related as polycubes are related to polyominoes. In origami, a polypolyhedron is "a compound...
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contemporary artists". The Art Directors of Philadelphia awarded him the Polycube Award for "consistent excellence in communications". The City of Milan...
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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...
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of scientific advances in fields as diverse as musical similarity,[MMS] polycube unfolding,[CUP] computational archaeology,[WBT] and protein folding. Langerman's...
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chapters of the first edition concern generalizations of polyominoes to polycubes and other polyforms, and briefly mention the work of Edward F. Moore and...
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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...
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coplanar misses from sections of the cubic honeycomb (alternatively convex polycubes) or alternated cubic honeycomb, ignoring any obscured faces. Examples:...
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