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Interactive Visualization and Verification Tools for Tesseract Path Unfoldings (Media Exposition)

Authors Soham Samanta, Hugo A. Akitaya , Erik Demaine , Martin Demaine

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LIPIcs.SoCG.2026.104.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • unfolding
  • polyominoes
  • tesseract
  • path unfolding
  • visualization

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Abstract

This paper introduces interactive software tools for studying 2-face path unfoldings of the tesseract (4D hypercube). We present: (1) an algorithm to verify whether a given 24-omino is a valid path unfolding of the tesseract, (2) a web-based visualization tool for exploring and animating unfolding sequences with smooth 3D interpolation, and (3) a design interface integrated with SVG Painter, with a similar design to Demaine’s SVG Painter, to create custom unfoldings. We demonstrate these tools by designing a geometric font of 36 path unfoldings resembling Latin letters and digits, illustrating the rich diversity and accessibility of tesseract geometry.

Cite As Get BibTex

Soham Samanta, Hugo A. Akitaya, Erik Demaine, and Martin Demaine. Interactive Visualization and Verification Tools for Tesseract Path Unfoldings (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 104:1-104:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.104

Author Details

Soham Samanta
  • Greater Commonwealth Virtual School, Medford, MA, USA
Hugo A. Akitaya
  • University of Massachusetts Lowell, MA, USA
Erik Demaine
  • MIT CSAIL, Cambridge, MA, USA
Martin Demaine
  • MIT CSAIL, Cambridge, MA, USA

Funding

  • A. Akitaya, Hugo: Supported by the NSF award CCF-2348067.

Supplementary Materials

References

  1. Hugo A. Akitaya and Nithish V. Kandarpa. Unfolding skeletons. In Proc. 24th Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCGGG), 2022. Google Scholar
  2. Hugo A. Akitaya and Soham Samanta. Path-unfolding the tesseract. In Proc. 31st Fall Workshop on Computational Geometry, 2024. Google Scholar
  3. Erik D. Demaine. SVG Painter. URL: https://erikdemaine.org/svgpainter/.
  4. Erik D. Demaine and Joseph O'Rourke. Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press, 2007. Google Scholar
  5. Giovanna Diaz and Joseph O'Rourke. Hypercube unfoldings that tile ℝ³ and ℝ², 2015. URL: https://arxiv.org/abs/1512.02086.
  6. Ken Perlin. Improving noise. ACM Transactions on Graphics, 21(3):681-682, July 2002. URL: https://doi.org/10.1145/566654.566636.
  7. Soham Samanta, Hugo Akitaya, Erik Demaine, and Martin Demaine. 2-face path unfolding the tesseract into a font. In Proc. 32nd Fall Workshop on Computational Geometry, 2025. To appear. Google Scholar
  8. Peter D. Turney. Unfolding the tesseract. Journal of Recreational Mathematics, 17(1):1-16, 1984. Google Scholar
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