PreprintCC BY 4.0arXiv
Each simplex in ℝ4 has a point with at least $14$ emanating normals to its boundary
Abstract
We prove that each simplex in ℝ4 contains a point with at least $14$ emanating normals to the boundary. Earlier, the authors proved that each generic simple polytope in ℝ4 contains a point with at least $12$ emanating normals to the boundary. This problem belongs to a piecewise linear counterpart of a longstanding problem concerning normals to smooth convex bodies.
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BibTeX
@misc{nasonov2026each,
title = {{Each simplex in $\mathbbR^4$ has a point with at least $14$ emanating normals to its boundary}},
author = {Ivan Nasonov and Gaiane Panina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13475},
eprint = {2610.13475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13475},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Each simplex in ℝ^4 has a point with at least $14$ emanating normals to its boundary
AU - Ivan Nasonov
AU - Gaiane Panina
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13475
UR - https://arxiv.org/abs/2610.13475
AB - We prove that each simplex in ℝ^4 contains a point with at least $14$ emanating normals to the boundary. Earlier, the authors proved that each generic simple polytope in ℝ^4 contains a point with at least $12$ emanating normals to the boundary. This problem belongs to a piecewise linear counterpart of a longstanding problem concerning normals to smooth convex bodies.
ER -