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Pach’s Animal Problem Within the Bounding Box

Author Martin Tancer

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LIPIcs.SoCG.2024.78.pdf
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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Animal problem
  • bounding box
  • non-shellable balls

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Abstract

A collection of unit cubes with integer coordinates in ℝ³ is an animal if its union is homeomorphic to the 3-ball. Pach’s animal problem asks whether any animal can be transformed to a single cube by adding or removing cubes one by one in such a way that any intermediate step is an animal as well. Here we provide an example of an animal that cannot be transformed to a single cube this way within its bounding box.

Cite As Get BibTex

Martin Tancer. Pach’s Animal Problem Within the Bounding Box. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 78:1-78:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.78

Author Details

Martin Tancer
  • Department of Applied Mathematics, Charles University, Prague, Czech Republic

Funding

Supported by the GAČR grant no. 22-19073S.

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