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We find minimal and maximal length of intersections of lines at a fixeddistance to the origin with the cross-polytope. We also find maximal volumenoncentral sections of the cross-polypote by hyperplanes which are at a fixedlarge distance to the origin and minimal volume sections by symmetric slabs ofa large fixed width. This parallels recent results about noncentral sections ofthe cube due to Moody, Stone, Zach and Zvavitch.

A note on the extremal noncentral sections of the cross-polytope