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Shape made from cubes joined together
A polycube is an orthogonal polyhedron formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar
Polycube
Solid with six equal square faces
results in a truncated cube. Joining one or more cubes face-to-face yields a polycube, a three-dimensional version of polyominoes. Two or more cubes can have
Cube
Four squares connected edge-to-edge
and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected
Tetromino
Four-dimensional analogue of the cube
Space? Retrieved 2025 May 11. Langerman, Stefan; Winslow, Andrew (2016). Polycube Unfoldings Satisfying Conway's Criterion (PDF). 19th Japan Conference on
Tesseract
Every natural number can be represented as the sum of four integer squares
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
Lagrange's four-square theorem
Lagrange's_four-square_theorem
Programming technique on linked lists
The dancing links algorithm solving a polycube puzzle
Dancing_links
Polyhedron in which all edges are parallel
axis-parallel, thus Jessen's icosahedron is not an orthogonal polyhedron. Polycubes are a special case of orthogonal polyhedra that can be decomposed into
Orthogonal_polyhedron
Solid-dissection 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
Soma_cube
Geometric shape formed from five squares
divided into nine pentominoes, as shown. [citation needed] A pentacube is a polycube of five cubes. Of the 29 one-sided pentacubes, exactly twelve pentacubes
Pentomino
Flat-sided three-dimensional shape
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
Polyhedron
Geometric shape formed from squares
Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study
Polyomino
Natural number
(ed.). "Sequence A000162 (Number of three dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS
23_(number)
Online database of integer sequences
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
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Three-dimensional packing puzzle
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
Diabolical_cube
Three-dimensional packing puzzle
Iljasov on 25 February 2008. Slothouber–Graatsma puzzle Conway puzzle Polycube Soma cube GB patent 2183166, Leslie James Heaton, "Puzzle cubes", published
Bedlam_cube
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
1000_(number)
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
Tripod_packing
2D shape constructed by joining together identical basic polygons
joined along congruent faces. Joining cubes in this way produces the polycubes, and joining tetrahedrons in this way produces the polytetrahedrons. 2-dimensional
Polyform
Abstract strategy board game whose pieces are polyominoes
unlike in Blokus "2D": The pieces are four times the eleven possible polycubes of two, three, and four (unit) cubes. A piece must be placed such that
Blokus
1989 video game
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
Blockout
Natural number
{\displaystyle \textstyle \left\{{11 \atop 2}\right\}} . There are 1023 polycubes with 7 cells (when counting reflections as distinct, which is standard)
1023_(number)
Edge-joined polygon with multiple principle shapes
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
Common_net
Subdivision of space into cells
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;
Mesh_generation
Three-dimensional packing puzzle
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
Herzberger_Quader
American graphic designer (1925–2018)
contemporary artists". The Art Directors of Philadelphia awarded him the Polycube Award for "consistent excellence in communications". The City of Milan
Art_Paul
Armenian mathematician, teacher and author (1928–2006)
also produced hands-on teaching materials including workbooks for the polycube. He also drew upon insights into pedagogy in the writings of Mary Boole
Dikran_Tahta
3D geometric figure formed from squares
is an example of a hexominoid, or 6-cell polyominoid, and many other polycubes have polyominoids as their boundaries. Polyominoids appear to have been
Polyominoid
Three-dimensional packing problem
Slothouber–Graatsma puzzle is an example of a cube-packing puzzle using convex polycubes. More general puzzles involving the packing of convex rectangular blocks
Slothouber–Graatsma_puzzle
Belgian computer scientist and mathematician
of scientific advances in fields as diverse as musical similarity,[MMS] polycube unfolding,[CUP] computational archaeology,[WBT] and protein folding. Langerman's
Stefan_Langerman
Textbook on the use of group theory in studying tessellations
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
Algebra_and_Tiling
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
List of Martin Gardner Mathematical Games columns
List_of_Martin_Gardner_Mathematical_Games_columns
Centered figurate number representing an octahedron
19th centuries. His "Haüy construction" approximates an octahedron as a polycube, formed by accreting concentric layers of cubes onto a central cube. The
Centered_octahedral_number
Convex polyhedron whose faces are almost regular polygons
coplanar misses from sections of the cubic honeycomb (alternatively convex polycubes) or alternated cubic honeycomb, ignoring any obscured faces. Examples:
Near-miss_Johnson_solid
3D building and strategy board game whose pieces are polycubes
the number of players. The pieces are four sets of the eleven possible polycubes composed of two, three, and four (unit) cubes. In each set, each block
Rumis
Polyhedron which tiles 3D space
with a Dehn invariant of zero that do not tile space (such as various polycubes). Hilbert's eighteenth problem, one of Hilbert's problems, consisting
Space-filling_polyhedron
Mathematical game
higher dimensions: for example, Player 1 may be trying to form a particular polycube on a 3D grid while Player 2 tries to stop him. The 2x2 square tetromino
Harary's generalized tic-tac-toe
Harary's_generalized_tic-tac-toe
Book on shapes formed from squares
chapters of the first edition concern generalizations of polyominoes to polycubes and other polyforms, and briefly mention the work of Edward F. Moore and
Polyominoes: Puzzles, Patterns, Problems, and Packings
Polyominoes:_Puzzles,_Patterns,_Problems,_and_Packings
American mathematician
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
Sherman_K._Stein
(disambiguation) Shuffling playing cards Pochhammer symbol Polyforms Polycubes Soma cube Polyiamonds Polyominoes Hexominoes Pentominoes Tetrominoes Polysquare
Index of combinatorics articles
Index_of_combinatorics_articles
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Boy/Male
Irish
nollaig is the Irish word for Christmas and is given to boys or girls born on December 25th.
Girl/Female
German
From the North
Surname or Lastname
English
English : habitational name from Buckminster in Leicestershire, named with the Old English personal name Bucca (see Buck) + Old English mynster ‘minster’, ‘large church’.
Girl/Female
Arabic, Muslim
Smell Like Saffron; Wonderful Smell
Boy/Male
Indian, Sanskrit, Telugu
Goodness
Girl/Female
Hindu, Indian
Name of God
Boy/Male
British, English, Hungarian
Lord; God's Own; Belonging to Lord
Surname or Lastname
English
English : habitational name, probably from Waldridge in County Durham (probably named with Old English wall ‘wall’ + hrycg ‘ridge’). However, in the British Isles, the surname is most common in Suffolk; it may be that another place similarly named, but lost, is the origin.
Girl/Female
Indian
Island
Girl/Female
Hindu, Indian
Lord Murugan Wife
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