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On Polyhedra with Rhombic Vertices and Regular Faces

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In this paper, we consider the class of closed convex polyhedra with regular faces in E3 for which the stars of some vertices are symmetric and consist of equal and identically located rhombuses (RR-polyhedra). We obtain a complete classification of RR-polyhedra with two acute-angled rhombic vertices whose stars are separated by a belt of regular faces of the same type. The proof is based on a result on the existence of two polyhedra of this class obtained by the author earlier.

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Correspondence to V. I. Subbotin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 181, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 3, 2020.

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Subbotin, V.I. On Polyhedra with Rhombic Vertices and Regular Faces. J Math Sci 276, 802–806 (2023).

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