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Updated: Jan 15, 2026

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Towards a taxonomy of nets: supersymmetric 2- and 3-periodic structures in three-dimensional Euclidean space
Mian Li1, Michael O'Keeffe2, Michael M J Treacy3
1Department of Chemistry, Shantou University, Shantou, Guangdong 515063, People's Republic of China.
Abstract:
Supersymmetric structures are defined as edge-transitive spatial graphs where the order of the site symmetry at each vertex is at least twice the coordination number of the vertex. Only 11 vertex- and edge-transitive connected periodic graphs possess this property, which we describe. We identify 32 examples of supersymmetric vertex 2-transitive, edge-transitive nets, also detailed here. Additionally, we list supersymmetric interpenetrating and interwoven structures, including weavings and polycatenanes.
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