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Petty's equilateral-set conjecture in dimension five

  • Kaiwen Yang
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Abstract

Petty conjectured that every n-dimensional real normed space contains n+1 equidistant points. The conjecture was proved in dimensions three and four by Petty and Makeev, respectively. We prove the five-dimensional case: every five-dimensional real normed space contains six equidistant points. The proof uses a bordism of equilateral configurations and a homological obstruction.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026pettys,
  title = {{Petty's equilateral-set conjecture in dimension five}},
  author = {Kaiwen Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39967},
  eprint = {2610.39967},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39967},
}
RIS
TY  - UNPB
TI  - Petty's equilateral-set conjecture in dimension five
AU  - Kaiwen Yang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39967
UR  - https://arxiv.org/abs/2610.39967
AB  - Petty conjectured that every n-dimensional real normed space contains n+1 equidistant points. The conjecture was proved in dimensions three and four by Petty and Makeev, respectively. We prove the five-dimensional case: every five-dimensional real normed space contains six equidistant points. The proof uses a bordism of equilateral configurations and a homological obstruction.
ER  -