PreprintarXiv licencearXiv
Unfolding Overlaps of the Exceptional Regular Polytopes
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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BibTeX
@misc{devadoss2026unfolding,
title = {{Unfolding Overlaps of the Exceptional Regular Polytopes}},
author = {Satyan L. Devadoss and Matthew Harvey and David Richter},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30285},
eprint = {2608.30285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30285},
}
RIS
TY - UNPB
TI - Unfolding Overlaps of the Exceptional Regular Polytopes
AU - Satyan L. Devadoss
AU - Matthew Harvey
AU - David Richter
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30285
UR - https://arxiv.org/abs/2608.30285
AB - 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.
ER -