Key points are not available for this paper at this time.
We construct a convex body K in Rⁿ, n 5, with the property that there is exactly one hyperplane H passing through c (K), the centroid of K, such that the centroid of K H coincides with c (K). This provides answers to questions of Gr\"unbaum and Loewner for n 5. The proof is based on the existence of non-intersection bodies in these dimensions.
Myroshnychenko et al. (2024) studied this question.