Geodesic
On a class of polyhedra with symmetrical vertex stars
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 88-97.

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The influence of the local symmetry of stars of some vertices of a closed convex polyhedron in $E^3$ on its geometry is considered. A theorem on the complete classification of symmetric polyhedra some of whose vertices possess symmetric stars od deltoid or rhombic faces is proved. In the proof, we use so-called strongly symmetric polyhedra and the lemma on local symmetry conditions previously introduced by the author.
Keywords: convex polyhedron, vertex star, strongly symmetric polyhedron, $FS$-polyhedron, deltoid vertex, $RDS$-polyhedron.
Mots-clés : rhombic vertex 
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V. I. Subbotin. On a class of polyhedra with symmetrical vertex stars. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 88-97. http://geodesic.mathdoc.fr/item/INTO_2019_169_a10/

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