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Unfolding Overlaps of the Exceptional Regular Polytopes

Satyan L. Devadoss, Matthew Harvey, David Richter

Source record

Source: arXiv

Published: Aug 31, 2026

arXiv: 2608.30285

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Source abstract

We find explicit ridge unfoldings of the three exceptional 4D polytopes (24-cell, 120-cell, 600-cell) that result in overlaps of their facets. These failures bring an end to the full classification of regular polytopes with the all-net property.

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Unfolding Overlaps of the Exceptional Regular Polytopes — Mathematical Frontier Network