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A variant of the Circle Packing Theorem states that the combinatorial class of any convex polyhedron contains elements midscribed to the unit sphere centered at the origin. Mani strengthened this result by showing the existence of such a polyhedron with the additional property that the barycenter of the tangency points is the origin. The aim of this paper is to show that this statement remains true if we replace the barycenter of the tangency points by other polyhedron centers.

Centering Koebe polyhedra via Möbius transformations