Bilbao Crystallography Server

Bilbao crystallographic server. II: Representations of crystallographic point groups and space groups. The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line ( The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc·). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group–subgroup relations between space groups (subgroups and supergroups, Wyckoff-position splitting schemes etc·). There are also software packages studying specific problems of solid-state physics, structural chemistry and crystallography. This article reports on the programs treating representations of point and space groups. There are tools for the construction of irreducible representations, for the study of the correlations between representations of group–subgroup pairs of space groups and for the decompositions of Kronecker products of representations.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Jorgensen, Jeremy J.; Christensen, John E.; Jarvis, Tyler J.; Hart, Gus L. W.: A general algorithm for calculating irreducible Brillouin zones (2022)
  2. van den Berg, Jan Bouwe; Williams, J. F.: Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem (2021)
  3. Xu, Nan; Doerschuk, Peter: Computation of real-valued basis functions which transform as irreducible representations of the polyhedral groups (2021)
  4. Chelnokov, Grigory; Mednykh, Alexander: The enumeration of coverings of closed orientable Euclidean manifolds (\mathcalG_3) and (\mathcalG_5) (2020)
  5. Gui-Bin Liu, Miao Chu, Zeying Zhang, Zhi-Ming Yu, Yugui Yao: SpaceGroupIrep: A package for irreducible representations of space group (2020) arXiv
  6. Chelnokov, G.; Deryagina, M.; Mednykh, A.: On the coverings of Euclidean manifolds (\mathcalB_1) and (\mathcalB_2) (2017)
  7. Grimmer, Hans: Thermoelectric transport properties in magnetically ordered crystals (2017)
  8. Aroyo, Mois I.; Orobengoa, Danel; de la Flor, Gemma; Tasci, Emre S.; Perez-Mato, J. Manuel; Wondratschek, Hans: Brillouin-zone database on the \textitBilbaoCrystallographic Server. (2014)
  9. Okuyan, Erhan; Güdükbay, Uğur; Gülseren, Oğuz: Pattern information extraction from crystal structures (2007)
  10. Aroyo, Mois I.; Kirov, Asen; Capillas, Cesar; Perez-Mato, J. M.; Wondratschek, Hans: Bilbao crystallographic server. II: Representations of crystallographic point groups and space groups (2006)
  11. Hauswirth, Laurent; Pérez, Joaquín; Romon, Pascal; Ros, Antonio: The periodic isoperimetric problem (2004)
  12. Ros, Antonio: Isoperimetric inequalities in crystallography (2004)