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Original Articles

Counting Crystallographic Groups in Low Dimensions

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Pages 407-411 | Published online: 04 Apr 2012

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Jürgen Opgenorth. (2001) Dual Cones and the Voronoi Algorithm. Experimental Mathematics 10:4, pages 599-608.
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Carlos Cid & Tilman Schulz. (2001) Computation of Five-and Six-Dimensional Bieberbach Groups. Experimental Mathematics 10:1, pages 109-115.
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Franka Miriam Brückler & Vladimir Stilinović. 2020. Handbook of the History and Philosophy of Mathematical Practice. Handbook of the History and Philosophy of Mathematical Practice 1 42 .
Akinari Hoshi, Ming-chang Kang & Aiichi Yamasaki. (2023) Multiplicative Invariant Fields of Dimension ≤6. Memoirs of the American Mathematical Society 283:1403.
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Alejandro Tolcachier. (2022) Classification of 6-dimensional splittable flat solvmanifolds. manuscripta mathematica 170:3-4, pages 531-561.
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Franka Miriam Brückler & Vladimir Stilinović. 2020. Handbook of the History and Philosophy of Mathematical Practice. Handbook of the History and Philosophy of Mathematical Practice 1 42 .
Alejandro Tolcachier. (2022) $$G_2$$-structures on flat solvmanifolds. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 92:2, pages 179-207.
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Dietrich Burde. (2021) Crystallographic actions on Lie groups and post-Lie algebra structures. Communications in Mathematics 29:1, pages 67-89.
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Paweł Piwek, David Popović & Gareth Wilkes. (2021) Distinguishing crystallographic groups by their finite quotients. Journal of Algebra 565, pages 548-563.
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S Groot Nibbelink. (2020) Nonexistence of locally but not globally supersymmetric orbifolds. Journal of Physics: Conference Series 1586:1, pages 012030.
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Stefan Groot Nibbelink, Orestis Loukas, Andreas Mütter, Erik Parr & Patrick K. S. Vaudrevange. (2020) Tension Between a Vanishing Cosmological Constant and Non‐Supersymmetric Heterotic Orbifolds. Fortschritte der Physik 68:7.
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Renato G. Bettiol, Andrzej Derdzinski & Paolo Piccione. (2018) Teichmüller theory and collapse of flat manifolds. Annali di Matematica Pura ed Applicata (1923 -) 197:4, pages 1247-1268.
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R. Veysseyre, D. Weigel, T. Phan & H. Veysseyre. (2015) Crystallography in Spaces E<sup>2</sup>, E<sup>3</sup>, E<sup>4</sup>, E<sup>5</sup> ...N<sup>0</sup>I Isomorphism Classes: Properties and Applications to the Study of Incommensurate Phase Structures, Molecular Symmetry Groups and Crystal Families of Space E<sup>5</sup. Advances in Pure Mathematics 05:04, pages 137-149.
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. 2014. Introduction to Crystal Growth and Characterization. Introduction to Crystal Growth and Characterization 1 170 .
Nansen Petrosyan & Bartosz Putrycz. (2012) On cohomology of crystallographic groups with cyclic holonomy of split type. Journal of Algebra 367, pages 237-246.
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Michael James Downward. (2011) Crystallographic point groups in five dimensions. Zeitschrift für Kristallographie 226:1, pages 32-39.
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John G Ratcliffe & Steven T Tschantz. (2010) Fibered orbifolds and crystallographic groups. Algebraic & Geometric Topology 10:3, pages 1627-1664.
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Bernd Souvignier. (2006) The four-dimensional magnetic point and space groups. Zeitschrift für Kristallographie - Crystalline Materials 221:1, pages 77-82.
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Bettina Eick & Bernd Souvignier. (2005) Algorithms for crystallographic groups. International Journal of Quantum Chemistry 106:1, pages 316-343.
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E. Molnár, I. Prok & J. Szirmai. (2003) D-V cells and fundamental domains for crystallographic groups, algorithms, and graphic realizations. Mathematical and Computer Modelling 38:7-9, pages 929-943.
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