Affine invariant points and new constructions
Abstract
In branko Gr\"unbaum asked if the set of all affine invariant points of a given convex body is equal to the set of all points invariant under every affine automorphism of the body. In ivan we have proven the case of a body with no nontrivial affine automorphisms. After some partial results (aip,newaip) the problem was solved in positive by Mordhorst Olaf. In this note we provide an alternative proof of the affirmative answer, developing the ideas of ivan. Moreover, our approach allows us to construct a new large class of affine invariant points.
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