On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space

V. N. Berestovskii; Yu. G. Nikonorov

On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space

Metric Geometry 2025-12-10 v3

Authors: V. N. Berestovskii , Yu. G. Nikonorov

Abstract

This paper is devoted to the study of the $m$ -point homogeneity property for the vertex sets of polytopes in Euclidean spaces. In particular, we present the classifications of $2$ -point and $3$ -point homogeneous polyhedra in $\mathbb{R}^3$ .

Keywords

homogeneous polyhedra Euclidean space vertex sets polytopes m-point homogeneity

Cite

@article{arxiv.2408.09911,
  title  = {On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space},
  author = {V. N. Berestovskii and Yu. G. Nikonorov},
  journal= {arXiv preprint arXiv:2408.09911},
  year   = {2025}
}

Comments

36 pages, 22 figures. New sources have been added to the bibliography along with corresponding comments. Some inaccuracies and typos have been corrected

On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space

Abstract

Keywords

Cite

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