A note on sphere containment orders

Using the ideas of Scheinerman and Wierman [1] and of Hurlbert [2] we give a very short proof that the infinite order [2]×[3]× cannot be represented by containment of Euclidean balls in ad-dimensional space for anyd. Also we give representations of the orders [2]×[2]× and [3]×[3]×[3] by containment of circles in the plane.The work was financially supported by the Russian Foundation of Fundamental Research, Grant 93-011-1486