Classification of isosceles 7-point 3-distance sets in 3-dimensional Euclidean space
type: Item
instance of: scholarly article
title: Classification of isosceles 7-point 3-distance sets in 3-dimensional Euclidean space
zbMATH Open document ID: 1121.51010
author: Hiroaki Kido
published in: European Journal of Combinatorics
publication date: 2007-03-27T00:00:00Z
review text: A subset \(X\) of the \(k\)-dimensional Euclidean space \(\mathbb{R}^k\) that contains \(n\) points is called an isosceles \(n\)-point \(s\)-distance set if there are exactly \(s\) distances between two distinct points in \(X\) and if every triplet of points selected from them forms an isosceles triangle. Evidently there are a lot of questions for existence of these special point-structures depending on \(k\), \(n\) and \(s\). Beforehand the author gives a short summary about known facts. The main result of this paper is the classification of all isosceles 7-point 3-distance sets in \(\mathbb{R}^3\): There exist exactly fifteen isomorphic-classes. Besides a multitude of properties of distance sets are discussed.
Mathematics Subject Classification ID: 51K05
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 5137575
zbMATH Keywords: distance geometry
zbMATH Keywords: \(s\)-distance set
zbMATH Keywords: \(P(n)\)-set
zbMATH Keywords: isosceles \(n\)-point \(s\)-distance set
reviewed by: Erhard Quaisser
MaRDI profile type: Publication
full work available at URL: j.ejc.2006.01.003
OpenAlex ID: W1972820816
cites work: Q3211358
cites work: An upper bound for the cardinality of an s-distance subset in real Euclidean space. II
cites work: Q3663319
cites work: 9-Point and 7-Point Configurations in 3-Space
cites work: Q5521940
cites work: Classification of isosceles eight-point sets in three-dimensional Euclidean space
cites work: On Two-Distance Sets in Euclidean Space
cites work: New maximal two-distance sets
cites work: Classification of three-distance sets in two dimensional Euclidean space
DOI: 10.1016/J.EJC.2006.01.003
description: scientific article; zbMATH DE number 5137575