PreprintCC BY 4.0arXiv
A short polyhedral proof of the infinitesimal Stoker conjecture
Abstract
The infinitesimal Stoker conjecture states that an infinitesimal deformation of a convex polytope that preserves all dihedral angles also preserves all normal directions up to isometry. We give a short polyhedral proof, self-contained up to assuming spectral and geometric properties of the Izmestiev matrix.
Related
- A Short Proof of Zhang's Conjecture on Stack-Sortable Permutations
- A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane
- A short proof of the Erd\H os--Sós Conjecture
- A short proof of the Segal conjecture for Cp
- A Short Proof of a Conjecture Regarding Quadratic Representations of Practical Numbers
BibTeX
@misc{winter2026short,
title = {{A short polyhedral proof of the infinitesimal Stoker conjecture}},
author = {Martin Winter},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14645},
eprint = {2609.14645},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14645},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A short polyhedral proof of the infinitesimal Stoker conjecture
AU - Martin Winter
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14645
UR - https://arxiv.org/abs/2609.14645
AB - The infinitesimal Stoker conjecture states that an infinitesimal deformation of a convex polytope that preserves all dihedral angles also preserves all normal directions up to isometry. We give a short polyhedral proof, self-contained up to assuming spectral and geometric properties of the Izmestiev matrix.
ER -