Power invariants of joined coaxial prisms

The paper is the addition to the article of Yu. Babenko and V. Zalgaller published in the same volume. A criterion indicating when the set in $\mathbb R^3$ of all vertices of several coaxial prisms inscribed in a sphere has power invariants $I_1,\dots,I_n$ is given. A finite set in $\mathbb R^3$ with 11 invariants is constructed. If invariants with alternating signs are admitted, it is proved that using joined prisms one can obtain finite sets in $\mathbb R^3$ with any preassigned number $n$ of invariants.