Two classes of compact convex polyhedra in E3 are introduced: RS- and RR-polyhedra. The stars of some vertices of each polyhedron in these classes consist of equal rhombi. In addition to the complete enumeration of RS-polyhedra, a proof of the existence of two polyhedra of the class RR is given.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 476, 2018, pp. 153–164.
Translated by V. I. Subbotin.
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Subbotin, V.I. On Two Classes of Polyhedra with Rhombic Vertices. J Math Sci 251, 531–538 (2020). https://doi.org/10.1007/s10958-020-05114-3
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DOI: https://doi.org/10.1007/s10958-020-05114-3