Infinite serie of extreme Delaunay polytopes

A Delaunay polytope P is said to be extreme if the only (up to isometries) affine bijective transformations f of Rn, for which f(P) is again a Delaunay polytope, are the homotheties. This notion was introduced in (Sets, Graphs and Numbers, Budapest (Hungary) (1991); Colloquia Mathematica Societatis János Bolyai 60 (1992) 157); also some examples in dimension 1, 6, 7, 15, 16, 22, 23 were constructed and it was proved there, that in dimension less than 6 there are no extreme Delaunay polytopes, except the segment. In this note, for every n≥6 we build an extreme Delaunay polytope EDn of dimension n.