Abstract
What is the largest cardinal of a two-by-two equilateral point-set in an n-dimensional Minkowski space? It is conjectured that this cardinal is at least $$n+1$$, and several spaces are tight in this regard, such as the Euclidean space. In this paper, we prove in normed spaces X with the $$(H_1,\dots ,H_{n-1})$$-2-intersection property the existence of $$n+1$$ equilateral point-sets of large diameter inscribed to the unit ball B. This extends the construction of Makeev (J Math Sci (N Y) 140:548–550, 2007) in dimension 4.
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