2021/12/11 by G. Domokos, Domokos, G., Z. Lángi +3
Mathematics · #52B10 #52B15 #74G05 #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2112.06079
openalex publication_date 2021/12/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Answering a question of Conway and Guy in a 1968 paper, Lángi in 2021 proved the existence of a monostable polyhedron with n-fold rotational symmetry for any n ≥ 3, and arbitrarily close to a Euclidean ball. In this paper we strengthen this result by characterizing the possible symmetry groups of all mono-monostatic smooth convex bodies and convex polyhedra. Our result also answers a stronger version of the question of Conway and Guy, asked in the above paper of Lángi.