Abstract

A Delaunay polytope P is said to be extreme if the only (up to isometries) affine bijective transformations f of R n , 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 ED n of dimension n.

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