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Power invariants of a union of coaxial prisms. (English. Russian original) Zbl 1003.51009
J. Math. Sci., New York 110, No. 4, 2769-2773 (2002); translation from Zap. Nauchn. Semin. POMI 261, 31-39 (1999).
Summary: The paper is an addition to the paper of Yu. I. Babenko and V. A. Zalgaller [see the paper above]. It gives a condition under which the set of all vertices of several coaxial prisms inscribed in a sphere in \(\mathbb{R}^3\) has power invariants \(I_1,\dots,I_n\). A finite set in \(\mathbb{R}^3\) with 11 invariants is constructed. It is also proved that unions of prisms yield finite sets in \(\mathbb{R}^3\) with any preassigned number \(n\) of invariants with alternating signs.
51M04 Elementary problems in Euclidean geometries
52A99 General convexity