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Zap. Nauchn. Sem. POMI, 2018, Volume 476, Pages 153–164 (Mi znsl6732)  

On two classes of polyhedra with rhombic vertices

V. I. Subbotin

South-Russian State Polytechnic University named M. I. Platov, Novocherkassk, Russia

Abstract: Two classes of closed convex polyhedra in $E^3$ ($RS$- and $RR$-polyhedra) are introduced; the stars of some vertices of the polyhedra under consideration consist of equal rhombi. In addition to the complete enumeration of $RS$-polytopes, the proof of the existence of two polyhedra of the class $RR$ is given.

Key words and phrases: strongly symmetric polyhedron, rhombic vertex, mirror-rotational rotation axis, $ TE $ -transformation, $RS$ - and $RR$-polyhedra.

Full text: PDF file (195 kB)
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UDC: 514.113.5
Received: 06.07.2018

Citation: V. I. Subbotin, “On two classes of polyhedra with rhombic vertices”, Geometry and topology. Part 13, Zap. Nauchn. Sem. POMI, 476, POMI, St. Petersburg, 2018, 153–164

Citation in format AMSBIB
\Bibitem{Sub18}
\by V.~I.~Subbotin
\paper On two classes of polyhedra with rhombic vertices
\inbook Geometry and topology. Part~13
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 476
\pages 153--164
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6732}


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