Geodesic
On polyhedra with rhombic vertices and regular faces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 112-117

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In this paper, we consider the class of closed convex polyhedra with regular faces in $E^3$ 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.
Keywords: convex polyhedron, symmetric rhombic vertex, star of the vertex, belt of regular faces, $RR$-polyhedron. 
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     author = {V. I. Subbotin},
     title = {On polyhedra with rhombic vertices and regular faces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {112--117},
     publisher = {mathdoc},
     volume = {181},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_181_a12/}
}
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V. I. Subbotin. On polyhedra with rhombic vertices and regular faces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 112-117. http://geodesic.mathdoc.fr/item/INTO_2020_181_a12/