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Symmetry of Structures That Can Be Approximated by Chains of Regular Tetrahedra

Symmetry of Structures That Can Be Approximated by Chains of Regular Tetrahedra Abstract The noncrystallographic symmetries of chains of regular tetrahedra are determined by mapping the system of algebraic geometry and topology designs to the structural level. It has been shown that the basic structural unit of such a chain is a tetrablock: a seven-vertex linear aggregation over faces of four regular tetrahedra, which is implemented in linear (right- and left-handed) and planar versions. The symmetry groups of linear and planar tetrablocks are isomorphic, respectively, to the projective special linear group PSL(2, 7) of order 168 and the projective general linear group PGL(2, 7) of order 336. A class of structures formed by an assembly of tetrablocks having no common tetrahedra is introduced. Examples of tetrablock assembly over common face, leading to a Boerdijk–Coxeter helix, an α helix, and a helix used as one of collagen models are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Crystallography Reports Springer Journals

Symmetry of Structures That Can Be Approximated by Chains of Regular Tetrahedra

Crystallography Reports , Volume 64 (3): 9 – May 1, 2019

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References (42)

Publisher
Springer Journals
Copyright
2019 Pleiades Publishing, Inc.
ISSN
1063-7745
eISSN
1562-689X
DOI
10.1134/s106377451903026x
Publisher site
See Article on Publisher Site

Abstract

Abstract The noncrystallographic symmetries of chains of regular tetrahedra are determined by mapping the system of algebraic geometry and topology designs to the structural level. It has been shown that the basic structural unit of such a chain is a tetrablock: a seven-vertex linear aggregation over faces of four regular tetrahedra, which is implemented in linear (right- and left-handed) and planar versions. The symmetry groups of linear and planar tetrablocks are isomorphic, respectively, to the projective special linear group PSL(2, 7) of order 168 and the projective general linear group PGL(2, 7) of order 336. A class of structures formed by an assembly of tetrablocks having no common tetrahedra is introduced. Examples of tetrablock assembly over common face, leading to a Boerdijk–Coxeter helix, an α helix, and a helix used as one of collagen models are presented.

Journal

Crystallography ReportsSpringer Journals

Published: May 1, 2019

Keywords: Crystallography and Scattering Methods

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