A Higher Dimensional Description of the Structure of β-Mn

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.

Keywords

• octagonal quasicrystal
• approximant
• six-dimensional space