Simplexes in normed space

Abstract

Is it true that, every subset of n + 1 points in Rn may be isomerticaly embedded in every n-dimensional real normed space. Answer is unknown to author for n ≥ 3. For n = 2 positive answer is evident. For n = 3 the problem is reduced to the case, when 4 points are in plane. Some reduction is made for every given n. Refs 4.