Interactive 2D Periodic Graphs (Media Exposition)

Authors Alexandra Camero , Ileana Streinu

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Author Details

Alexandra Camero
  • University of Massachusetts - Amherst, MA, USA
Ileana Streinu
  • Smith College, Northampton, MA, USA

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Alexandra Camero and Ileana Streinu. Interactive 2D Periodic Graphs (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 63:1-63:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We present an educational web app for interactively drawing and editing 2D periodic graphs. The user defines the unit cell and the finite set of vertex and edge representatives, from which a sufficiently large fragment of the periodic graph is created for the visualization. The periodic graph can also be modified by applying several transformations, including isometries and relaxations of the unit cell. A finite representation of the infinite periodic graph can be saved in an external file as a quotient graph with Z²-marked edges. Its geometry is recorded using fractional (crystallographic) coordinates. The facial structure of non-crossing periodic graphs can be revealed by the user interactively selecting face representatives. An accompanying video demonstrates the functionality of the web application.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Periodic graphs
  • isometric transformations


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  2. Ciprian S. Borcea and Ileana Streinu. Minimally rigid periodic graphs. Bulletin of the London Mathematical Society, 43(6):1093-1103, 2011. URL:
  3. Ciprian S. Borcea and Ileana Streinu. Frameworks with crystallographic symmetry. Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 372(2008), December 2013. URL:
  4. Ciprian S. Borcea and Ileana Streinu. Geometric auxetics. Proceedings of the Royal Society A, 471(20150033), December 2015. URL:
  5. Ciprian S. Borcea and Ileana Streinu. Liftings and stresses for planar periodic frameworks. Discrete and Computational Geometry, 53(4):747-782, June 2015. URL:
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  7. Jeff Erickson and Patrick Lin. A toroidal Maxwell-Cremona-Delaunay correspondence. Journal of Computational Geometry, 12(2), 2022. URL:
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