AI 中文总结
本文证明立方体切片可由其图唯一确定，并构造反例说明该性质不适用于一般简单多胞体。
AI 中文摘要
我们证明，在立方体切片的类别中，由超平面切割立方体所得的切片的组合类型完全由其图决定。我们还通过构造一个具有两个组合类型不同但图同构的切片的简单多胞体，表明这样的结果不能推广到任意简单多胞体的切片。
英文摘要
We prove that the combinatorial type of a slice of the cube by a hyperplane is completely determined by its graph, within the class of cube slices. We also show that such a result cannot extend to slices of arbitrary simple polytopes by constructing a simple polytope that has two combinatorially distinct slices with isomorphic graphs.
