Symmetry and Topology: The 11 Uninodal Planar Nets Revisited
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 tra...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-01-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/2/35 |
| _version_ | 1818036946377637888 |
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| author | Jean-Guillaume Eon |
| author_facet | Jean-Guillaume Eon |
| author_sort | Jean-Guillaume Eon |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T07:19:02Z |
| format | Article |
| id | doaj.art-4b436d70478d4b71ae1a6cf6fd746f0f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T07:19:02Z |
| publishDate | 2018-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4b436d70478d4b71ae1a6cf6fd746f0f2022-12-22T01:57:51ZengMDPI AGSymmetry2073-89942018-01-011023510.3390/sym10020035sym10020035Symmetry and Topology: The 11 Uninodal Planar Nets RevisitedJean-Guillaume Eon0Institute of Chemistry, Federal University of Rio de Janeiro, Avenida Athos da Silveira Ramos, 21941-909 Rio de Janeiro, BrazilA 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.http://www.mdpi.com/2073-8994/10/2/35uninodal netscrystal structuressymmetrylabeled quotient graphs |
| spellingShingle | Jean-Guillaume Eon Symmetry and Topology: The 11 Uninodal Planar Nets Revisited Symmetry uninodal nets crystal structures symmetry labeled quotient graphs |
| title | Symmetry and Topology: The 11 Uninodal Planar Nets Revisited |
| title_full | Symmetry and Topology: The 11 Uninodal Planar Nets Revisited |
| title_fullStr | Symmetry and Topology: The 11 Uninodal Planar Nets Revisited |
| title_full_unstemmed | Symmetry and Topology: The 11 Uninodal Planar Nets Revisited |
| title_short | Symmetry and Topology: The 11 Uninodal Planar Nets Revisited |
| title_sort | symmetry and topology the 11 uninodal planar nets revisited |
| topic | uninodal nets crystal structures symmetry labeled quotient graphs |
| url | http://www.mdpi.com/2073-8994/10/2/35 |
| work_keys_str_mv | AT jeanguillaumeeon symmetryandtopologythe11uninodalplanarnetsrevisited |