Symmetry 2012, 4(3), 537-544; doi:10.3390/sym4030537
Article

A Higher Dimensional Description of the Structure of β-Mn

1,* email and 2email
Received: 3 July 2012; in revised form: 22 August 2012 / Accepted: 22 August 2012 / Published: 27 August 2012
(This article belongs to the Special Issue Crystal Symmetry and Structure)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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MDPI and ACS Style

Lidin, S.; Fredrickson, D. A Higher Dimensional Description of the Structure of β-Mn. Symmetry 2012, 4, 537-544.

AMA Style

Lidin S, Fredrickson D. A Higher Dimensional Description of the Structure of β-Mn. Symmetry. 2012; 4(3):537-544.

Chicago/Turabian Style

Lidin, Sven; Fredrickson, Daniel. 2012. "A Higher Dimensional Description of the Structure of β-Mn." Symmetry 4, no. 3: 537-544.

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