Structure of a group related to a Napoleon tessellation
type: Item
instance of: scholarly article
title: Structure of a group related to a Napoleon tessellation
zbMATH Open document ID: 1288.51011
DOI: 10.4171/EM/214
author: Vlastimil Dlab
published in: Elemente der Mathematik
publication date: 2013-10-08T00:00:00Z
review text: In this paper, the author presents a comprehensive description of the structure of the polyhedral group (G) using a geometric representation. He demonstrates two interesting theorems: 1) Let \(S_{N}\) be the symmetry group of the Napoleon tesselation. The mapping \( {\Psi}:G{\rightarrow} S_{N},{\Psi}(a)=R_{(0,0)} \) and \({\Psi}(b)=R_{(0,1)}\) is an isomorphism of the groups G and \(S_{N}\); 2) If H is the free abelian group of rank 2 and K is the cyclic group of order 3, then H corresponds to the normal subgroup of all translations of \(S_{N} \) and \(K=<{\Psi}^{-1}(R_{(0,0)})>\).
reviewed by: Cătălin Barbu
Mathematics Subject Classification ID: 51M15
zbMATH DE Number: 6213891
zbMATH Keywords: Napoleon tesselation
zbMATH Keywords: symmetry group
Wikidata QID: Q105658131
MaRDI profile type: Publication
cites work: Q3273607
cites work: Q5343413
cites work: Napoleon, Escher, and Tessellations
full work available at URL: https://doi.org/10.4171/em/214
OpenAlex ID: W2077164624
description: scientific article; zbMATH DE number 6213891