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Symmetry 2018, 10(2), 35; https://doi.org/10.3390/sym10020035

Symmetry and Topology: The 11 Uninodal Planar Nets Revisited

Institute of Chemistry, Federal University of Rio de Janeiro, Avenida Athos da Silveira Ramos, 21941-909 Rio de Janeiro, Brazil
Received: 9 January 2018 / Revised: 20 January 2018 / Accepted: 22 January 2018 / Published: 24 January 2018
(This article belongs to the Special Issue Mathematical Crystallography)
Full-Text   |   PDF [1523 KB, uploaded 24 January 2018]   |  

Abstract

A description of the 11 well-known uninodal planar nets is given by Cayley color graphs or alternative Cayley color graphs of plane groups. By applying methods from topological graph theory, the nets are derived from the bouquet B n with rotations mostly as voltages. It thus appears that translation, as a symmetry operation in these nets, is no more fundamental than rotations. View Full-Text
Keywords: uninodal nets; crystal structures; symmetry; labeled quotient graphs uninodal nets; crystal structures; symmetry; labeled quotient graphs
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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 (CC BY 4.0).
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Eon, J.-G. Symmetry and Topology: The 11 Uninodal Planar Nets Revisited. Symmetry 2018, 10, 35.

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