A higher dimensional description of the structure of \(\beta\)-Mn
type: Item
instance of: scholarly article
title: A higher dimensional description of the structure of \(\beta\)-Mn
zbMATH Open document ID: 1351.52026
author: Sven Lidin
author: Daniel Fredrickson
published in: Symmetry
publication date: 2016-12-09T00:00:00Z
review text: Summary: The structure of \(\beta\)-Mn crystallizes in space group \(\text P4_132\). The pseudo 8-fold nature of the \(4_1\) axes makes it constitute an approximant to the octagonal quasicrystals. In this paper we analyze why a five-dimensional super space group containing mutually perpendicular 8-fold axes cannot generate \(\text P4_132\) on projection to 3-d space and how this may instead be accomplished from a six-dimensional model. A procedure for generating the actual structure of \(\beta\)-Mn lifted to six-dimensional space is given.
Mathematics Subject Classification ID: 52C23
zbMATH DE Number: 6662263
zbMATH Keywords: octagonal quasicrystal
zbMATH Keywords: approximant
zbMATH Keywords: six-dimensional space
MaRDI profile type: Publication
full work available at URL: sym4030537
OpenAlex ID: W2046823556
cites work: Character table of the hypercubic point group in six dimensions
DOI: 10.3390/SYM4030537
description: scientific article; zbMATH DE number 6662263