A higher dimensional description of the structure of \(\beta\)-Mn
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.
scientific article; zbMATH DE number 6662263