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arXiv · 2112.06079

A characterization of the symmetry groups of mono-monostatic convex bodies

G. Domokos·Z. Lángi·P. Várkonyi
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Abstract

Answering a question of Conway and Guy in a 1968 paper, L\'angi in 2021 proved the existence of a monostable polyhedron with $n$-fold rotational symmetry for any $n \geq 3$, 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 L\'angi.

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G. Domokos, Z. Lángi, P. Várkonyi. 2021-12-11. A characterization of the symmetry groups of mono-monostatic convex bodies. https://arxiv.org/abs/2112.06079

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