Visualizing and Unfolding Nets of 4-Polytopes (Media Exposition)

Authors Satyan L. Devadoss, Matthew S. Harvey, Sam Zhang

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Author Details

Satyan L. Devadoss
  • Department of Mathematics, University of San Diego, CA, USA
Matthew S. Harvey
  • Department of Mathematics and Computer Science, University of Virginia’s College at Wise, VA, USA
Sam Zhang
  • Department of Applied Mathematics, University of Colorado Boulder, CO, USA

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Satyan L. Devadoss, Matthew S. Harvey, and Sam Zhang. Visualizing and Unfolding Nets of 4-Polytopes (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 67:1-67:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Over a decade ago, it was shown that every edge unfolding of the Platonic solids was without self-overlap, yielding a valid net. Recent work has extended this property to their higher-dimensional analogs: the 4-cube, 4-simplex, and 4-orthoplex. We present an interactive visualization that allows the user to unfold these polytopes by drawing on their dual 1-skeleton graph.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Applied computing → Computer-assisted instruction
  • unfoldings
  • nets
  • polytopes


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