Periodic Structures and Crystal Chemistry
In the rationalization process of complex structures it is very helpful the “topological approach” that consists in the simplification by rational principles of the complex structures to schematized reference nets. A higher level of complexity comes from the entanglement of different periodic motifs whose rationalization and classification we have illustrated in the last years. The different branches of mathematics involved show the interdisciplinary approach of the Topological Crystal Chemistry developed in the Samara Center for Theoretical Material Science (SCTMS) www.sctms.ru
simplification and rationalization -> nets (graph theory)
topological classification/analysis of nets[2,3]
- single/entangled/catenated/knotted (knot theory)[4,5]
- enumeration of nets and relation to carbon allotropes [6,7]
- tiling theory and zeolites 
 "What do we know about three periodic nets." O. Delgado-Friedrichs, M.D. Foster, M. O'Keeffe, D.M. Proserpio, M.M.J. Treacy, O.M. Yaghi J. Solid State Chem. 2005, 178, 2533-2554.
 "Underlying nets in three-periodic coordination polymers: topology, taxonomy and prediction from a computer-aided analysis of the Cambridge Structural Database" E. V. Alexandrov, V.A. Blatov, A.V. Kochetkov, D.M. Proserpio CrystEngComm, 2011, 13, 3947-3958.
 "Applied Topological Analysis of Crystal Structures with the Program Package ToposPro" V.A. Blatov, A.P. Shevchenko, D.M. Proserpio Cryst. Growth Des. 2014, 14, 3576-3586.
"Entangled Two-Dimensional Coordination Networks: A General Survey" L. Carlucci, G. Ciani, D. M. Proserpio, T.G. Mitina, V.A. Blatov Chem. Rev. 2014, 114, 7557–7580.
 Interpenetrating metalorganic and inorganic 3D networks: a computer aided systematic investigation. Part I. Analysis of the Cambridge structural databaseV.A. Blatov, L. Carlucci, G. Ciani, D.M. Proserpio CrystEngComm, 2004, 6, 377-395.
 "From zeolite nets to sp3 carbon allotropes: a topology-based multiscale theoretical study" I.A. Baburin, D.M. Proserpio, V.A. Saleev and A.V. Shipilova Phys. Chem. Chem. Phys., 2015, 17, 1332-1338
 "Homo Citans and Carbon Allotropes: For an Ethics of Citation" R. Hoffmann, A.A. Kabanov, A.A. Golov, D.M. Proserpio Angew. Chem. Int. Ed. 2016 in press DOI: 10.1002/anie.201600655R1
 "The zeolite conundrum: Why are there so many hypothetical zeolites and so few observed? A possible answer from the zeolite-type frameworks perceived as packings of tiles" V.A. Blatov, G.D. Ilyushin, D.M. Proserpio Chem. Mater. 2013, 25, 412-424.