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 noncentral sections of the cross-polypote 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 noncentral sections of the cube due to Moody, Stone, Zach and Zvavitch.

中文翻译：

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关于交叉多面体的极值非中心部分的说明

我们找到了距离原点固定距离的线与交叉多面体相交的最小和最大长度。我们还通过与原点有固定大距离的超平面找到了交叉多囊动物的最大体积非中心部分，并通过大固定宽度的对称板找到了最小体积部分。这与穆迪、斯通、扎克和兹瓦维奇最近关于立方体非中心部分的结果相似。