Tiling \({\mathbb{R}}^ 3\) with circles and disks
We say that Euclidean n-space \({\mathbb{R}}^ n\) admits a tiling by a family of sets if every point of \({\mathbb{R}}^ n\) belongs to exactly one set of the family. The author proves that \({\mathbb{R}}^ 2\) does not admit a tiling by a family of homeomorphs of a disk and that \({\mathbb{R}}^ 3\) admits a tiling by a family of rhombi with edge length 1. The question is put if \({\mathbb{R}}^ 3\) can be tiled by a family of congruent squares.
scientific article; zbMATH DE number 4126192