Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
tiling of n-dimensional space by hypercubes
|
| gptkbp:debunkedBy |
gptkb:Lagarias_and_Shor
|
| gptkbp:disprovedInYear |
1992
|
| gptkbp:field |
gptkb:geometry
gptkb:mathematics |
| gptkbp:formedBy |
gptkb:Ott-Heinrich_Keller
1930 |
| https://www.w3.org/2000/01/rdf-schema#label |
Keller's conjecture
|
| gptkbp:relatedTo |
combinatorics
cube tiling face-sharing cubes lattice tilings |
| gptkbp:sentence |
In any tiling of n-dimensional Euclidean space by unit cubes, there are two cubes that share a complete (n−1)-dimensional face.
|
| gptkbp:status |
disproved in dimension 10 and higher
false in dimension 8 and higher true for dimensions up to 6 |
| gptkbp:bfsParent |
gptkb:Ott-Heinrich_Keller
|
| gptkbp:bfsLayer |
5
|