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DOI: 10.4230/LIPIcs.SoCG.2026.104

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

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

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

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.

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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)

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@InProceedings{samanta_et_al:LIPIcs.SoCG.2026.104,
  author =	{Samanta, Soham and A. Akitaya, Hugo and Demaine, Erik and Demaine, Martin},
  title =	{{Interactive Visualization and Verification Tools for Tesseract Path Unfoldings}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{104:1--104:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.104},
  URN =		{urn:nbn:de:0030-drops-259104},
  doi =		{10.4230/LIPIcs.SoCG.2026.104},
  annote =	{Keywords: unfolding, polyominoes, tesseract, path unfolding, visualization}
}

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

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