Tiling \({\mathbb{R}}^ 3\) with circles and disks
type: Item
instance of: scholarly article
title: Tiling \({\mathbb{R}}^ 3\) with circles and disks
zbMATH Open document ID: 0687.52009
DOI: 10.1007/BF00147430
author: J. B. Wilker
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 4126192
zbMATH Keywords: circle
zbMATH Keywords: rhombus
zbMATH Keywords: Euclidean n-space
zbMATH Keywords: tiling
zbMATH Keywords: disk
reviewed by: Marek Lassak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147430
OpenAlex ID: W2073915708
description: scientific article; zbMATH DE number 4126192