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A Higher Dimensional Description of the Structure of β-Mn

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Author(s): Sven Lidin | Daniel Fredrickson

Journal: Symmetry
ISSN 2073-8994

Volume: 4;
Issue: 3;
Start page: 537;
Date: 2012;
Original page

Keywords: octagonal quasicrystal | approximant | six-dimensional space

ABSTRACT
The structure of β-Mn crystallizes in space group P4132. The pseudo 8-fold nature of the 41 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 P4132 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 β-Mn lifted to six-dimensional space is given.
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