A note on the extremal non-central sections of the cross-polytope

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