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- Keller's_conjecture abstract "In geometry, Keller's conjecture is the conjecture introduced by Ott-Heinrich Keller (1930) that in any tiling of Euclidean space by identical hypercubes there are two cubes that meet face to face. For instance, as shown in the illustration, in any tiling of the plane by identical squares, some two squares must meet edge to edge. This was shown to be true in dimensions at most 6 by Perron (1940a, 1940b). However, for higher dimensions it is false, as was shown in dimensions at least 10 by Lagarias and Shor (1992) and in dimensions at least 8 by Mackey (2002), using a reformulation of the problem in terms of the clique number of certain graphs now known as Keller graphs. Although this graph-theoretic version of the conjecture is now resolved for all dimensions, Keller's original cube-tiling conjecture remains open in dimension 7.The related Minkowski lattice cube-tiling conjecture states that, whenever a tiling of space by identical cubes has the additional property that the cube centers form a lattice, some cubes must meet face to face. It was proved by György Hajós in 1942.Szabó (1993), Shor (2004), and Zong (2005) give surveys of work on Keller's conjecture and related problems.".
- Keller's_conjecture thumbnail Shifted_square_tiling.svg?width=300.
- Keller's_conjecture wikiPageExternalLink b34h1sza.ps.gz.
- Keller's_conjecture wikiPageID "33297462".
- Keller's_conjecture wikiPageRevisionID "549649403".
- Keller's_conjecture author1Link "Jeffrey Lagarias".
- Keller's_conjecture author2Link "Peter Shor".
- Keller's_conjecture authorlink "Oskar Perron".
- Keller's_conjecture authorlink "Ott-Heinrich Keller".
- Keller's_conjecture first "Ott-Heinrich".
- Keller's_conjecture hasPhotoCollection Keller's_conjecture.
- Keller's_conjecture last "Keller".
- Keller's_conjecture last "Lagarias".
- Keller's_conjecture last "Perron".
- Keller's_conjecture last "Przesławski".
- Keller's_conjecture last "Shor".
- Keller's_conjecture last "Łysakowska".
- Keller's_conjecture year "1930".
- Keller's_conjecture year "1940".
- Keller's_conjecture year "1992".
- Keller's_conjecture year "2008".
- Keller's_conjecture year "2011".
- Keller's_conjecture subject Category:Conjectures.
- Keller's_conjecture subject Category:Cubes.
- Keller's_conjecture subject Category:Parametric_families_of_graphs.
- Keller's_conjecture subject Category:Tessellation.
- Keller's_conjecture type Abstraction100002137.
- Keller's_conjecture type Attribute100024264.
- Keller's_conjecture type Cognition100023271.
- Keller's_conjecture type Concept105835747.
- Keller's_conjecture type Conjectures.
- Keller's_conjecture type Content105809192.
- Keller's_conjecture type Cube113916721.
- Keller's_conjecture type Cubes.
- Keller's_conjecture type Hypothesis105888929.
- Keller's_conjecture type Idea105833840.
- Keller's_conjecture type Polyhedron113883885.
- Keller's_conjecture type PsychologicalFeature100023100.
- Keller's_conjecture type RegularPolyhedron113915999.
- Keller's_conjecture type Shape100027807.
- Keller's_conjecture type Solid113860793.
- Keller's_conjecture type Speculation105891783.
- Keller's_conjecture comment "In geometry, Keller's conjecture is the conjecture introduced by Ott-Heinrich Keller (1930) that in any tiling of Euclidean space by identical hypercubes there are two cubes that meet face to face. For instance, as shown in the illustration, in any tiling of the plane by identical squares, some two squares must meet edge to edge. This was shown to be true in dimensions at most 6 by Perron (1940a, 1940b).".
- Keller's_conjecture label "Conjecture de Keller".
- Keller's_conjecture label "Keller's conjecture".
- Keller's_conjecture sameAs Conjecture_de_Keller.
- Keller's_conjecture sameAs m.0h7px1w.
- Keller's_conjecture sameAs Q4802474.
- Keller's_conjecture sameAs Q4802474.
- Keller's_conjecture sameAs Keller's_conjecture.
- Keller's_conjecture wasDerivedFrom Keller's_conjecture?oldid=549649403.
- Keller's_conjecture depiction Shifted_square_tiling.svg.
- Keller's_conjecture isPrimaryTopicOf Keller's_conjecture.
