%0 Journal Article
%T A Higher Dimensional Description of the Structure of ¦Â-Mn
%A Sven Lidin
%A Daniel Fredrickson
%J Symmetry
%D 2012
%I MDPI AG
%R 10.3390/sym4030537
%X The structure of ¦Â-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 ¦Â-Mn lifted to six-dimensional space is given.
%K octagonal quasicrystal
%K approximant
%K six-dimensional space
%U http://www.mdpi.com/2073-8994/4/3/537