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Polycube

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 polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes.

Octacube and hypercube unfoldings, Enumerating polycubes & Boundary connectivity

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Explore the main themes, entities and connections around Polycube. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Octacube and hypercube unfoldings

TesseractHypercubeFacetsUnfoldedHexomino
13 related topics

Enumerating polycubes

ChiralMirror reflectionOEIS
3 related topics

Boundary connectivity

ManifoldPolyominoidOpen problem
3 related topics

Dual graph

Dual polyhedronDual graph
2 related topics

Topics to explore

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Overview

Enumerating polycubes

Symmetries of polycubes

Properties of pentacubes

Octacube and hypercube unfoldings

Boundary connectivity

Dual graph

Advanced semantic analysis

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Map overview Semantic statistics

Polycube

Nodes40
Edges39
Triples31
Avg. degree1.95
Density0.05
Components1

How this topic connects Entity context

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Polycube

Top relations

related to External links · 12
Polycube → Algorithm, Commons STL, George, Gong, KadonSicherman, Kevin, Lepage, Lua, Marc, Polycube Symmetries, Program, Wooden
related to Enumerating polycubes · 6
Polycube → For, In, Like, Polycubes, Soma, Unlike
related to Boundary connectivity · 5
Polycube → Although, For, If, It, That
related to Symmetries of polycubes · 4
Polycube → As, Lunnon, Most, There
related to Dual graph · 3
Polycube → Dual, The, This
is a · 1
Polycube → orthogonal polyhedron formed by joining one or more equal cubes face to face

Important terminology Word statistics

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Important terminology

polycubes cubes boundary one cube pentacubes polyominoes also chiral mirror symmetry symmetries dual graph orientations cross connected unfolded octacube enumerated

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polycubeis aorthogonal polyhedron formed by joining one or more equal cubes face to face0.90text
Polycuberelated to Boundary connectivityAlthough0.60section
Polycuberelated to Boundary connectivityFor0.60section
Polycuberelated to Boundary connectivityIt0.60section
Polycuberelated to Boundary connectivityIf0.60section
Polycuberelated to Boundary connectivityThat0.60section
Polycuberelated to Dual graphThe0.60section
Polycuberelated to Dual graphThis0.60section
Polycuberelated to Dual graphDual0.60section
Polycuberelated to Enumerating polycubesLike0.60section
Polycuberelated to Enumerating polycubesFor0.60section
Polycuberelated to Enumerating polycubesUnlike0.60section

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